ZOHAN... long time no talk!!... So let me chime in here...
It's odd that the primary breaker is tripping without any issues on the secondary breakers. The scenario could be that there is something getting into the transformer- mouse, chipmunk, etc. that has eaten some insulation and is causing that to happen. Second scenario is that the secondary breaker is bad, not tripping when it should, and thus the primary trips, but only after the core heats up enough to cause the trip.
So as the other guys said.... check the amperage of each run and make sure you are within your range for the circuit. ( SOmeone could have put 50 watt lamps in where there should be 20's)
If your lines measure out ok, test the secondary breaker by creating a short with a loop of wire... see if that causes the secondary breaker to trip. If not, then the problem could be the secondary breaker.
Next, check the voltage at the outlet. I'm doing some math here and wonder if the transformer is being fed with lower than normal voltage on the line voltage side, if the current draw of the primary fuse/breaker would be elevated. ( Maybe their AC or something is kicking on and drawing the voltage down)
WHen you make the trip, bring a spare 25 amp breaker or fustat and socket... also.. bring a 5 amp buss fuse with holder to use on the primary side... in case you find either breakers not to be working properly.
As a test, you could disconnect the primary breaker and put the buss fuse in it's place.. see what happens.
I'm a little puzzled because you say it's a 300 watt transformer that has multiple breakers on the 12 volt side??
If you end up opening the transformer cabinet, check the push on terminal connectors on the breakers. I've had a lot of situations where that stay-kon connector gets loose, hot and eventually loosens over time which creates arcing... but then again.. that would result in the primary breaker tripping.
Well.. good luck... hope this helps.. keep us posted