Yes, Nehemiah asked God four times to remember his deeds, and twice to remember his enemies.

Throughout the book of Nehemiah, Nehemiah continued to be a good servant-leader and did many good deeds for the people.  For as it happened in those days most leaders would lay burdens on the people, collect taxes from them, and then would force them to sell their land, which they could no longer afford (Neh. 5:15-16).  But Nehemiah refused to lay unfair burdens on the people.  Instead he served the people and helped them build the temple walls.  Likewise, when other nobles and rulers took advantage of them he would put a stop to it (Neh. 5:3-12).  And when the people needed to be corrected and rebuked, Nehemiah took on that responsibility as well (Neh. 13:4-30).

And for all his efforts in service and leadership he did not ask for any rewards from the people; but he prayed four times, “Remember me,” for he knew that only God could give him a true and lasting reward.

1.  Nehemiah 5:19

Remember me, my God, for good, according to all that I have done for this people.

2.  Nehemiah 13:14

Remember me, O my God, concerning this, and do not wipe out my good deeds that I have done for the house of my God, and for its services!

3.  Nehemiah 13:22b

Remember me, O my God, concerning this also, and spare me according to the greatness of Your mercy!

4.  Nehemiah 13:31

Remember me, O my God, for good!

Also (in Neh. 6:14 and 13:29) he asks God to remember those who were against him and against Israel, for he knew that only God would deal justly with His enemies.

5.  Nehemiah 6:14

My God, remember Tobiah and Sanballat, according to these their works, and the prophetess who would have made me afraid.

6.  Nehemiah 13:29

Remember them, O my God, because they have defiled the priesthood and the covenant of the priesthood and the Levites.