There are three levels of upkeep in WC3. No, low, and high (names could be something else). They happen at some set used supply number. Lets say 30 and 60. 0 - 29 will be no upkeep, 30 - 59 will be low upkeep, and 59 - max (99?) will be high. Each of these brackets cost you more gold to maintain, which is taken from each worker when they return from the mine. For this, you typically won't want to ever get past a low upkeep. This shouldn't be a problem if you're playing the game right.
Upkeep won't stop you from building units though, that's just a supply cap. Either you need to make more farms/burrows/zigs/wells or you're at 99/99.