There's no correlation between leaving the PJ on "standby" & false starts. My HS10's been pretty much connected to the supply from day one nearly 10 months ago now.
It started it's "antics" at maybe 300 hours (like yours

) with the occassional false start, rising to 2 or 3 out of 5 being "false". Always started on the 2nd attempt (without unplugging). Gradually improved & I think its last false start was maybe 6 months ago.
Warranty nearly up? Then perhaps it's better to have Sony check it out - should get a new lamp at least, although that doesn't seem to have cured Comer's problem.
Chances are it'll subside over time, but IMO a call to Sony would be warranted.
Best of luck