The short answer is: maybe, but probably not.
To some extent the nature of the problem depends on the material you used for the rigging, and what (if anything) you did to the thread before you put it on the model.
There are two likely reasons for the problem: age, and changing environmental conditions. Some fabrics (e.g., cotton) tend to relax and stretch a little as they get older. If you rigged the model with cotton thread, and it's stretched, there's not a lot you can do about it. If you used the thread that came with the kit, I'm at a loss. I have no idea what that stuff is.
It's just as likely, though, that the sagging has been caused by a marked increase in humidity. If so, you might -
might - be able to get it to tighten up again by putting the model in a warm, extremely dry room for a while. (An electric dehumidifier might help.) Having tried such tricks on old models in the museum where I used to work, though, I'm frankly not really optimistic. Once thread stretches for any reason, it's tough to get it to "unstretch."
If you waxed the thread before you put it on the model, it should be less susceptible to humidity than it otherwise would be. In practical terms, that means it probably didn't stretch as much as unwaxed thread would have - but it won't respond much to any improvement in the environment either.
Somebody told me once, a long time ago, that thread could be made to shrink by brushing it with a solution of alum and water. I tried that once and it had no effect whatsoever - at least none I could see.
Maybe a physicist or chemist who reads this can offer a more sophisticated answer than I can, but I'm not optimistic. Even if you do find some means of tightening things up in general, it probably will be difficult to control. Whatever you do is likely, if it works at all, to tighten something up too much - and break something.
I wish I had a more helpful answer, but I'm afraid the only real solution is to rerig the lines that have gone slack.