It's usually due to variations in the moisture content of the thread. A trick that I've found often works is to wet the threads using a moistened Q-tip, and allow them to dry. As they dry out, they become taut again.
If you use cyanoacrylate glues, this won't be a problem. Cotton thread is really not what you should use. Good scale rope is available made out of polyester. It doesn't have the sagging problems. Silk is also a good choice. Silk thread in various thicknesses are available at any good sewing supply shop in many different colors.
I've got about the same amount of time with my CA. Guess we'll have to wait for the verdict from our grandchildren or their children. Actually, I use three: thinned Casein glue (e.g., Tightbond, Elmer's), CA (both thin and gap-filling) and so-called "rigging cement" which is also known as watchmaker's crystal cement.
Thinned Elmer's if for givng coiled lines a permanent shape and not for holding the line down.
There should be no knots unless the full-sized ship had such knots in those places. In other words, almost no knots. Knots are used for lines for which there will be cause to do and undo in the course of sailing. Such lines are very unheard of in the standing rigging and rare in the running rigging. The exception being the knots used to attach sail-hanks to sails or sails to stays, to hold reefing lines in place, and of-course, the clove hitches on the rat lines. The end attached to a block, spar, or eye should be served -- as they would be on the full-sized ship. If the scale is too small for that, a drop of CA will hold the two lines together at the block and a small dab of black paint will do for the serving. However, I find that at 48:1 or
50:1 or larger scale, all lines that should be served can be served. I usually serve lines with very thin, blackened, copper wire. (38 gauge or finer). The simplest source for such wires is to take apart the shielding on microphone cables, although the thin wire in lamp cord will also do. Blacken it with the appropriate blackening compound (e.g., liver of sulphur) I make it up in lengths of about 18" which is convenient to work with and I put it out of the shield bundle only as I need it. You'll find that serving with thin copper wire is much, much easier than serving with thread. Furthermore, it provides a much better scale appearance, even under a magnifying glass. Once the serving is done, a tiny drop of the thin CA finishes the job off.
The bitter end usually goes to a belaying pin. Now wrapping the line about the belaying pin, especially the last reversed loop, can be very difficult. I usually cheat there. I take the line through the belaying pin hole and then shove the pin in, adjusting the tension as I do so. Then a tiny drop of crystal cement finishes off the job. After the glue dries (about an hour or so) I snip off the bitter end and hang a pre-formed coil over the belaying pin to finish it off.
CA is wonderful for making "glue needles". A drop of thin CA about an inch long on the rigging line converts the end into a glue needle. With CA, it takes a few seconds, while other glues you'll have to wait an hour. A glue needle is much better than a sewing needle because if they line can get through, the glue needle will. A regular needle is much thicker and besides, there is the doubled thread -- for an over-all thickness of about four times the line. That means that threading through a small block, you'll break about half the blocks you attempt to use. With glue needles, that doesn't happen. The glue needle gets into places an ordinary needle can't possible get and furthermore, it can be bent into a hook for the really in-accessible cases. By comparison, the smallest curved surgical needle (e.g., used for eye surgery, is gross by comparison).
I've been doing less and less use of waxed thread. With glue needles, you don't need the added stiffness to get through blocks. Also, the lubricating properties of the wax, while occassionally useful, smears down the line strands so that goos scale three-strand line ends up looking like waxed thread instead of three-strand scale line. Also tends to be shiny, which is poor scale and obliterates detail. I think the idea of waxed thread is more tradition than necessity these days. For cotton thread used for rigging, wax greatly increases the strength of the line but for modern dacron scale lines, that's no issue. The line strength, even for very thin lines, is far greater than the spars can possibly take. The only place where wax is useful in my mind is when you want to get a realistic, scale droop to a particular line. I personally like the thinned elmers better for that purpose.