Ah, that is what is called a 'hot re-strike' and that can be a problem too. Short technical explanation follows:
As an HID lamp is truly an arc lamp, there must be a high enough voltage to initiate the arc. Once started, about 85 volts will maintain it but it requires upwards of 20,000 volts to start or strike the original arc. The small glass envelope that contains the arc has metal salts inside it (they look like brown sand when the bulb is cold) and once heated, they turn to gas and produce the huge amounts of light that HIDs put out and also cause the arc to the be color that it is. However, when those salts are hot and gasified, the electrical resistance inside the envelope goes up, making it harder to strike the arc in the first place. So shutting HIDs off and then restarting them while they are still hot (the 'hot re-strike') is the situation that takes the most voltage from the ballast. That is where some of the Chinese ballasts may fall down occasionally- not so much the ballast itself but the actual igniter (which is the part that provides the extremely high strike voltage). If that happens, all the while the light is off it is cooling down so the next restrike occurs at a lower (bulb) temperature when it will probably work. Hence the seemingly erratic behavior. You can help it along by making sure all the electrical connections are tight and not bound too tightly to any grounded surface (the arc will just as happily jump out of the cable through the insulation as across the HID's internal electrodes).
If it continues to be a problem, I would suggest contacting the store where you got them and as about getting a new ballast and igniter or even everything on that side of the bike in the event it is a bulb with unusual hot resistance causing the problem. If it is only very occasional, I would just ignore it and re-start the bike and the lights when it does happen.
By the way, speaking of the high starting voltage: be careful with handling HIDs and powering them up. They are not particularly dangerous IMO but unlike the original 12 volt wiring on the bike, you cannot be entirely cavalier with the wires, connections, and especially any open connections because that starting voltage is perfectly happy jumping out of the connector and into your hand(s) if there is not a complete connection.
As to your question of anything bad happening to the ballast if the HID fails to strike- nope, they are designed with that in mind so it is not a problem. Also, it is inevitable that vehicle lighting will be damaged and so it is expected that a ballast will try to ignite a lamp that is no longer there or not connected (front end damage from a vehicle accident is the most likely cause) so there are a set number of times that ballast will try to ignite the lamp and then shut itself down until the ballast itself is powered down and back up. This all happens in less than one second so there is no danger of the ballast overheating or similar. This is a case where the 'good' OEM ballasts are inferior in a way to the aftermarket things- after a certain number of tries (five I think), Hellas are designed to open an internal fuse and shut down permanently. Once that happens, the ballast will never power up again- it is a safety feature to deal with auto damage. Unfortunately the only way to fix it is by buying a new ballast and Hella ballasts are not $25 / pair :-(
Brian
That makes sense, thanks. Funny that in both of the observed failure cases, it was right after a long ride (more than 30 minutes), and a short stop (5 to 15 minutes). Seems like battery voltage should have been high then. Also, with the engine all warmed up, cranking it over was at a minimum. Plus, my battery was new at the beginning of this year, so it's in great shape.
So am I correct that if the bulb doesn't light, there's no load on the ballast, and therefore no risk of damaging a ballast? Not sure what's going on inside the ballast, from current flow perspective.
