There are several reasons why this could be happening. First, check to see that you haven't over tightened the lock screw(s) that hold the lock in the rifle. Next, are the caps in good condition and have they been properly stored? If the caps have been exposed to high humidity or allowed to get damp in a rain, they may not be any good. If you decide that the caps are not the problem, then, they are not getting a good strike from the hammer on the nipple. Check the nipple. Have you or someone else been dry firing your gun with no cap on the nipple? You can hammer the top of the nipple so that the cap does not fit on it properly and will not receive a propper strike from the hammer. If you determine that the nipple is in good condition, the hammer is your next concern. Is the hammer clean in the recess that strikes the cap? Use a toothbrush to get up in there and scrub out any dirt and gunk. Use a toothpick to scratch around up in there to see if an old spent cap is stuck in there in a bunch of crud that has collected in there. If the hammer is nice and clean, next check to see that it is falling freely and not binding somewhere along the side of the lockplate. An easy way to do this is to remove the lock from your gun, remove the hammer and use a candle to smoke the lockplate. Replace the hammer on the lock being careful not to smudge your soot coating. Carefully cock the hamer and use your finger to press on the trigger bar to release the hammer. Keep one finger on the hammer to ease it down to the "fired" position. Do not let if fly forward freely. Do this a couple of times and if it is rubbing on the lockplate, you will see it in the soot coating. If this is occurring, you can make a shim to put behind the hammer to keep it away from the lockplate or you can carefully file the back side of the hammer to give it enough room to operate without hitting the lockplate. If the hammer is not rubbing anywhere on the lockplate, the only thing left is to examine the inside of the lock to see if the tumbler is rubbing on the inside of the lockplate. This can be done initialy by simply carefully examining the lockplate in good light with some magnification. If you see any rubbing or can feel it, you can shim the tumbler so it doesn't rub. If you don't feel comfortable disassembling the lock to work on the inside, you may have to take it to a properly qualified gunsmith to have the work done. Last of all, reassemble your lock and replace it into your gun. Now look for any place that the hammer might be rubbing on the stock.
Once you have done all of this, the problem should be solved. I have never seen a bad spring on a T/C or a Lymon Hawken. Some of the less expensive Hawkens may have springs that go bad and have to be replaced. If you suspect that it is the main spring and it is a flat spring, as opposed to a coil spring, you will need a spring cramp to remove and replace the mainspring. Do not try to do it without a spring cramp or you will likely break the spring. BTW the correct word is CRAMP not clamp. I don't know why, it just is.
Good luck in solving your problem. If this hasn't been as helpful as I hope it is, another one of the folks who answer will have other ideas that could be better than mine.