In theory, it would be possible for Mace to have survived, through the use of his Force powers.
Although as pointed out, he would be short of a hand and a lightsaber, the first could be rectified by having a cybernetic replacement (like Anakin), and the second by building a new lightsaber. The problem is that being a Jedi, his only source of finance would have been the Jedi bank accounts, which presumably Palpatine would have had frozen, thus leaving Mace with no money and no shelter (unless there were emergency funds/hideouts that were unknown to Palpatine, although this is highly unlikely).
Other points to consider if Mace did survive:
Why did he not respond to the Jedi signal beacon, and communicate with Yoda/Bail/Obi-Wan ?
What was he doing during the following 20 years while the Empire grew and asserted its authority across the galaxy ?
Why did he not join the Rebel Alliance (which was pro-jedi) ?
Overall, i am personally inclined to believe that the shock of Anakin's betrayal, losing his hand, and the effect of Palpatine's Force lightning rendered him unable to utilize his powers in order to save himself, and thus died when his body hit whichever 'ground' level was below.