Sounds like something is resistive and heating up and making a bad
connection. Are you running any kind of high intensity lights that draw
more current than stock?
If both do this, then it's most likely not a problem with a bulb
connection
itself. More likely a relay problem, or something along those lines.
I'd pull the headlight relay and make sure the connectors are ok and
making good contact. Also make sure all the vehicle ground straps
in that area are ok and tight. If it still does it, I'd measure the
voltage
before and after the relay. Also flaked out circuit breakers can do
this
if they have been abused with high current bulbs. The more resistive
the relay or breaker, the hotter it runs. The hotter it runs, the more
damage to the device to the point they can have a meltdown.
BTW, after it does this,  feel if the headlight relay or breaker is
real hot.
Maybe it's just bad plug connections.. Pulling it and replacing will
clean
the "pins" to an extent. You could also add some de-oxit,  or whatever
to clean them up. If it's the relay contacts, you'll probably need a
new relay.
I don't know if you can take them apart to clean or whatever.. Might be

sealed..
MK

There is a Honda TSB for this.  The dealer just fixed our '03 Accord for
this problem and Honda covered the cost 100% even though we were well
past the warranty period.  The cause was some kind of electrical system
monitoring device failure.  They replaced the entire under-hood fuse box
assembly.