Alright so I've been tuning my guitar to drop d, drop c, etc. and I keep having to re-do everything multiple times because the strings get out of tune when I when i move on to the next strings. It didn't use to do this. What's going on?
Firstly, Floyd Rose or fixed bridge?

The change in string tensions will knock the strings out of tune,
So that's why some strings will go out of tune when you drop/ increase the tensions of other strings.
AdamG313 asked a good question. If it's a Floyd Rose, you should either reset it yourself or have a guitar shop do so. If it's fixed, you don't need to do anything with the bridge.

However, no matter which type of bridge, I have to advise you to readjust you truss rod. If you don't, your neck will eventually warp. Here's a decent article on it. http://www.athensmusician.net/archive/2001-05-01_geneimbody1.shtml