Same on Hi or Low? And this is happening to BOTH?
If on high - when the headlights go out, does the blue indicator light also go out?
If it does, the problem is in the system
If it does NOT, then problem more likely in the headlights (although you would have to believe that it would be unlikely both would suffer same issue at same time)
This is std Roadster (X) wiring? no Additional relays or anything? (I'm just going by your profile that Rocket Three X - is it indeed an X or ????)
So you replaced the Starter/Headlight relay, right (the 5-pin one)?
Did you replace the other headlight relay? (the 4-pin one - item 68 on the schematic)
Do your running lights (tail light) remain on? (that circuit also energizes that 4 pin relay with ignition on)