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.
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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.
78 (Karlovic)
R.Å tepanek - I.Karlovic (Davis cup 2009)
6:7, 7:6, 7:6, 6:7, 16:14
Match time 5:59