One of the things I find really frustrating is when my woven-in ends start coming undone.
Dritz Fray Check to use on a cut edge that I didn't want to fray. That's when it struck me that it would work when weaving in ends on my crocheting.
You can find Fray Check at fabric stores or in the sewing department of big craft stores. You'll want to test it on a piece of scrap yarn from your project first. It could darken the yarn or make it overly stiff when it's dry.
If it works on the scrap, apply it carefully to a woven-in end. I usually apply it to the cut end and about 1/4 inch back to really secure it.
I can't guarantee that your ends won't start unweaving, but it seems to help prevent or delay it.