There isn't a maximum number of aces that a tennis player can make in a single tennis match. For example, Wimbledon has no tie-breaker in the fifth set, so the fifth set is limitless, so there is no maximum number of aces.
In the first round of Wimbledon 2010 John Isner served up 112 aces against Nicolas Mahut. The match lasted over 11 hours and was played over the course of 3 days, with the fifth set score finishing 70-68. The longest competitive match ever played.
The world record for most aces in a match is held by John Isner, with 112 aces in a first round match against Nicolas Mahut at the 2010 Wimbledon Championships on June 22nd - 24th 2010 (Mahut holds second place with 102 in the same match); the match also holds several other Open Era records, including longest match, at over eleven hours in length, and most combined aces - 214 in total. The record for the fastest ace (as well as the fastest overall serve) is held by Andy Roddick who served a 155 mph (~249 km/h) ace against Vlamir Voltchkov during the 2004 Davis Cup.
Goran Ivanisevic notched up 212 aces during Wimbledon 2001.
R.Å tepanek - I.Karlovic (Davis cup 2009)
6:7, 7:6, 7:6, 6:7, 16:14
Match time 5:59
On the women's side that would be 48. On the men's side that would be 72.
Tennis - 7 (1st,2nd,3rd,4th,QF,SF,F)
14 grand slam singles
Greg Rusedski has never won a Grand Slam Event.
Don Budge has won 6 Grand Slam Singles Titles.