yes it can. either your breaker is gettin weak or your ballast is starting to go bad and draws more amps than the breaker can take. a 20 amp breaker can take bout 16 amp continuously..much more than that and it'll start "kickin" can you use a different outlet/breaker close by?!..thatll help determine which is goin bad
Sorry man, the quoted statement is incorrect. A 20 amp breaker by definition is a breaker that can take a load of 20 amps for an infinite amount of time (not infinite, but they have a long life span). Circuit breaker manufacturers publish the circuit breaker's trip curve which shows the (*take a breath*) the time until the breaker trips depending on the proportion between the nominal current (the one stated on the breaker) and the actual current going through the breaker. You can look for more info on the circuit breaker curve, but I guess you just wanna grow weed and not become an electric engineer. So let's get practical:
Measure the time interval between drops of the breaker. If there is a consistency - it's probably an overload.
Try to monitor things you turn on in the house and see if there is a connection between devices you turn on and the breaks. If the breaks occur totally randomly - you might have a short circuit somewhere in the apartment. Hope the new breaker does the job, if not refer to my comment. By the way, changing the breaker to a bigger value without changing the wiring is a stupid and dangerous thing to do, so check the value of the new breaker...
Sorry for the bad English, and for shoving my mr. know-electricity agenda upon your post.
Happy growing!