Very common question.  How do I keep my Floyd Rose in tune?  First let me say this, I genuinely believe that the Floyd Rose trem is one of the best guitar bridges on the market, even if you don't use it for its trem function.  When set up correctly, you should not have problems.  That being said, if it's not set up properly, you can have problems keeping the guitar in tune.  So if you're having issues, here's some things to look into. 

1)  Your most likely issue is the guitar's setup itself.  So before you assume it's the bridge, have the intonation, neck angle, etc checked.  If that's off, the bridge won't function correctly.

2)  The setup of the Floyd itself has 2 critical issues.  First, make sure it is level with the body.  See the picture. . .  Second, make sure the counter springs in the back aren't over or under rated.  If you use heavier strings, you may need 3 springs.  For lighter, you may need only 2.  Check with Floyd Rose for the best application for your setup.

3)  Check your hardware.  Make sure the intonation screws and saddle locks are very tight.  Make sure your locks at the nut are tight, but don't over-tighten the locks on the nut.   These do NOT have to be cranked over-tight. Over-tightening here, in my experience, can cause issues.  But otherwise, make sure everything is tightened down.

4)  If you have a "Licensed Floyd", check your knife edges.  "Licensed" versions tend to be made of softer metal to keep the cost down.  This leads to premature wearing down or chipping of the knife edge.  This can quickly cause the Floyd to work improperly.  Don't fret if you have issues here.  There's plenty of guides on the net for resolving this problem, although the best solution in my opinion is to replace the bridge at that point with an actual Floyd Rose product.  If you're not sure, if your Floyd is "Licensed," it will say so right on the top of the bridge.  Just look for the word "licensed."  Anything else is most likely a genuine Floyd product.