Does the cost for resetting your Trait points go up depending on how many times you've done it in the past or does it go up depending on your level or some other factor?
The cost for resetting trait points in PvE is 5 copper per point. As such, the cost for resetting them at level 80 is 3 silver and 50 copper. It doesn't matter how many times you do it, that cost at cap will remain the same.
Alternatively, your trait points reset when you use Training Manuals, so take advantage of the free reset when you buy a manual at levels 11, 40, and 60.
When playing Structured PvP, resetting your trait points is free.