Assuming these are new strings, are you stretching them before you lock the nut? Sounds to me like a case of the strings stretching.

Unlock the nuts on the neck, get it in tune with the tuners on the headstock, lock the nuts and fine tune it with the tuners on the bridge. If you've stretched out the strings pretty good before you lock the nuts, it should hold tune well. You shouldn't have to touch the tuners on the headstock again until you change strings. I rarely have to do any real tuning on my Floyds. If the strings are stretched and you're still having a problem, it may need an adjustment.

Not sure if you're full access or not, but if you are, you might want to ask some questions in the Ask a Guitar Tech section.

Edited to add: If you're talking about the bolts at the very back of the bridge, the only time that you should mess with them is when you're changing strings. They tighten the blocks that hold the strings in place.