I pretty much agree with Bottle Rocket that you are causing your own problems, here.
If an opponent dropshots you once or twice in a match, OK. SURPRISE! You run and do what you can. If the opponent dropshots you "every chance he gets" then the problem is yours.
Obviously, if he was not successful, he would not continue to dropshot you.
What to do about it.
Your choices include: dropshot back (if he stays back deep. Volley deep and force him to hit a low percentage passing shot or lob (you need good volley/overhead skills for this to work.
The best thing would be to watch for his patterns, motions/be observant/anticipate. Then get in quick and put the ball away before it drops below the net- This will cause him to stop doing that and try something else.
In addition, you should try some of the things mentioned above. Keep the ball deep, keep pressure on the opponent. Vary your shots so he can't get too comfortable hitting them back (change your shot paterns, spin, pace, speed...)
The best possible thing you can do is start a program for improving the weak aspects of your game (the ones opponents take advantage of).
Instead of just playing a game for fun, work with a partner on specific shots and tactics. Buy a book of drills and strategies and work on these things.
Good luck,
B