Assuming you have a starter immobiliser...
I have a 2000 V70 2wd wagon that had a similar problem.
When the weather changed in the fall, once in a while I had trouble with
starting. The engine kept turning over.
I would pull the key out, wait a few seconds, and then try again. (As
though I flooded a carburetor) It would then start.
I mentioned to the dealer...never heard of such problem. They suggested
using the other key for a while to see if the problem would continue. Their
thinking was the chip in the key for the vehicle immobiliser.
Same occurrences with the second key.
When the starting problem happened again, I pulled out the key, flipped it
over, put it back in and tried starting the car...it started immediately.
(Fluke!) The several other times when I could not start the car, I flipped
the key and it started...(personally, I think it was a fluke every time).
In the end, the dealer changed the antenna that is around the ignition
keyhole...been a few weeks and everything is fine.
Matt
First time owner, long time looker
Hope this helps.