Start by removing the hid system completely on the side at fault and replace a halogen lamp, see if it happens again. (by the way, get alotta fuses lol) Then start removing one bulb at a time from the headlamp assembly, you may find a faulty socket, at that point you need to inspect the socket.
Before you do this though, if you just did the hid kit it may be possible that you pinched wires from the harness reinstalling the light, inspect the headlamp harness for kinks or rips or something.
1999 Jeep Cherokee Classic
1999 Pontiac Trans Am
1985 Chevy Monte Carlo SS