What do you mean by the phrase "my bees go off completely"? If I could understand what you mean, I could probably help you understand the nature of the problem.
He is probably referring to the modelling lamp.
When the Alienbees fire, depending on the switch settings the modeling lamp will momentarily go out and will slowly come back up as the flash capacitors charge back up. By slowly I mean the flash takes 1 second or less to go from completely discharge to full charge so during that brief moment it would appear that the alienbees have turned off.
There is a switch on the back of the head that you can change to make the modelling lamp stay on all the time. I don't have my head in front of me at the moment so I can't tell you off the top of my head what switch it is. It might be labelled track or cycle, pretty sure it is one of those two, change the settings and you will find it.

