same problem here
I constantly find my N810 discharge during the night. this morning it was dead. i switched it on and instantly put the car charger in. it booted fine, hildon desktop came up, but after 2 minutes it suddenly died. reconnecting the charger brings nokia logo, then dies after 10 seconds. holding the power button and conecting the charger also brings up the blue corner light, but same thing - dies in 5-10 seconds. tried in-house charger - same thing.
I cannot believe its the battery (but hope it is battery not some internal problem).
now i have to wait for some ebay battery order since nokia doesnt sell N810 in our country