If your bridge is an Original Floyd Rose, it should function perfectly if properly installed and properly setup. Here are some things you can check that may be adjusted incorrectly or might be damaged.
Check to see if the base plate is sitting parallel with the top surface of the guitar. If it seems to be tilted forward, toward the pickups, then you need to tighten the springs and retune the guitar and check the tilt again. If it is tilted back toward the body of the guitar loosen the springs and retune the guitar. Repeat this procedure until the bridge sits level.
Make sure the nut is attached securely by tightening the nut attachment screws. This is critical for tuning stability.
Make sure the string clamps at the nut and bridge are very tight.
Make sure the saddle intonation screws are tight.
If these things have been done correctly and your bridge still does not come back to the proper pitch when using the tremolo, the knife-edges may be damaged. To check this you must remove the bridge. You can easily remove the bridge with the strings still clamped in the bridge by removing the tremolo springs. [Be sure to hold on to the bridge when removing the springs.] If you don't feel comfortable doing this, take the guitar to a good guitar repairman. Check the knife-edges. They should not be dull or rounded or chipped. If they don't seem sharp you can order a replacement base plate by contacting us here.
The dull knife edge is a rare problem on Floyd Rose Original bridges, but is more common on licensed bridges. If your bridge says, "Licensed under Floyd Rose Patents" or similar anywhere on it, this is a licensed bridge, and "not under our quality control." If your bridge is a licensed bridge, you should contact the manufacturer of your guitar for replacement parts.
If your tremolo is "floating" (i.e. you can pull up or push down on the tremolo arm) and you bend a string, the other strings will go slightly flat. This is normal operation. If you don't want this to happen you must block the tremolo so that you can't pull up on it (Edward Van Halen uses his Floyd blocked this way). When the bridge is mounted in this manner it is as stable as a fixed bridge for string bending but the trade off is the loss of subtle vibrato effects. This blocking should be done by a qualified guitar repairman.