i've been using 50 and 80lb tight lines and notice when i set the "mouse trap" i get line breaks. keeping the line tight like that allows the smaller sharks cruising around to run into and chafe your line. if i set it in freespool with the line under the freespool lever (applies enough tension to the line to prevent over runs and current from dragging it out) then anything running into it wont cut or chafe it because the line is not tight enough to allow the necessary friction.
also, go for a swim! check out the area you are fishing and see how shallow the sand bars run. if the second bar is only 5ft deep, chances are your main line is rubbing and its getting chafed that way.
for the heavier 400 or 500lb mono above the wire, i would definitely use crimps but for mainline connections, a palomar knot all the time. you can tie a palomar up to 150lb mono and a uni anything after that.
How about a little more info on the "sliding concrete weight"? What size is it? How is it rigged and how does it slide. Is there a chance that your line is coming in contact with the concrete weight? I've not heard of a "sliding concrete weigh" before. That's my first guess but in trouble shooting any problem, it's important that only one change is made and then your test procedure ( fishing ) is preformed. See if a change occurs and then try changing one other thing and test again. Try to keep all of the other factors constant. This means the distance from shore should remain as a constant. Try to keep slack out of your line. That can be a very important factor in cutoffs. Change wire leader length, change the weight to a less abrasive substance. Try attaching the weight with different material and at different distances from your bait, etc.
This is a great scientific experment and you are the scientist. Let us know what you discover. Good Luck!
Try using 10ft+ of #19 wire. then 15-20ft of 600lb mono with 2 crimps on each end then tape over the tag end and crimps.
If black tips and spinners are in the area, or even blue fish or macks they will cut your line.
In late feb we were getting cut off almost every bait we put out from the blacktips.
Also when you drop your baits, let them hit bottom then reel your slack in.
as far as hook set goes.
Circle hooks: Have a extra tight drag pre-set then just flip
the switch from free spool the hook will set itself.
no running or walking back needed just wind.
J hooks: Set your drag as tight as you can, then flip out of free spool when the shark goes on a strong run.
Run away from the shark with the rod on your shoulder, reel on your chest until the line gets tight.
You might have to hold your spool on both sides to get the max drag.
Then pump the reel to your lower abs like your doing sit ups until the fish starts taking drag
do not stop running and pumping until you feel the solid weight and drag is being taken.
SlasherX4 and I used to do the dual-running man to ensure hook set. 
You guys are great, thanks for the solutions!
I think I should address this a little better, the line break problem has essentially gone away. Since I want hard core results from all this experimenting I'm doing, I really can't deviate from what I've already committed to (Sharkark, you touched on this approach and I agree). But everyone is giving such awesome advice I can't help but say thanks. Let me take the time to address each one of your posts:
doc_josh I see what you mean about the weight position. The weight slides on the 400 lb. mono shock leader, so that can't be what is cutting the line. Important, none the less. I also like how you use 2 opposing weights to steady the line better. Thanks.
sharkkiller1 My rods have all roller guides, but none the less I took your advice and inspected it all in detail. Thankfully they don't appear to be the culprit, they all work very smoothly without and nicks or burrs. I will make it a point to try reeling through a knot under pressure, THAT makes a lot of sense! Thanks.
DanTheMan There were 2 different types of line breaks. One was clearly knot failure (now I'm crimping my terminal tackle to my line), but the rest were abrasion related. This is why I'm using black line on one rod, to hide it from the fish. If I have fewer cutoffs on the black line, then I know it's the fish targeting the brightly colored line under tension. We have the time of year in mind (hence the year long experiment) will DEFINITELY KEEP FISHING!!! Thanks.
lowprofile I've wanted to try the mousetrap system, I just haven't yet. Gotta make the proper weights for it. Our lines are loose enough to prevent chafe, so we see eye to eye on that. Since I'm crimping my main line onto the leader for this experiment, I'll have to try the palomar knot another time. But swimming was a great idea! We actually found some parts of the ocean floor that could be a problem, but it appears to be before the last sandbar. I'll have to paddle out with a snorkel and see what it looks like farther out. Thanks.
sharkark The "sliding concrete weight" is exactly what it sounds like, it's really nothing special. We got tired of trying to find lead to make weights with so I came up with the idea of using concrete. At $5 for 50 pounds, it's a real bargain compared to lead weights! We pour it into a Solo cup and put a loop of coat hanger wire in it to tie onto. Then, when we make our leaders, we put the shock leader through the eye of a snap swivel. We can then snap our weight onto it, and the 15 foot leader slides through the eye making less tension when the fish pick up the bait. Again, I agree with keeping things "constant" until we are happy with the conclusions. Thanks.
Jimmylevelwind You nailed it. This is how we have our terminal tackle set up, except we're using cable instead of wire. Not a big difference. And it's good to know that I'm not the only one getting these problems! If this was happening to you in February, it makes sense that this would also happen to us in January/February. We'll see if the black fishing line hides from the macks and bluefish. And the hook set advice? Much appreciated! We're in the process changing over to all circle hooks, so that will help things to be more consistent. This package just came in from Lindgren-Pittman yesterday.
Thanks again everyone! You're all Aces in my book!
grind down those barbs! LP hooks a pain in the ass to get out sometimes due to the huge barb. great for long lining but i use barbless all the time and never drop fish once hooked.
if your using circle hooks you shouldnt have to be running back and yanking on them. that often just pulls the hook out.
i drop my bait, set the drag tight enough to set the hook, turn the clicker on, and open the spool. when the shark runs with your bait, wait like 15 seconds for it to eat it, then slam the spool closed.
thats what i would do.
I think this video clearly shows how to best operate a circle hook. These guys demonstrate that proper hook set depends on the fish's movement to orient the hook point into the jaw and that attempts to set a circle hook can easily lead to lost fish.
http://www.youtube.com/watch?v=0-gk9-IXTjw
great video. It really shows how well a circle hook works and gives me some ideals on how to set up my baits. Cant wait to try it out.