I had an on and off stalling going into limp mode problem with my 1998 v70r.
The previous owner sold it to me cheap because of the issue. She had had it in the shop half a dozens times for it and it just kept happening to her.

Ultimately, I had to replace the front O2 sensor ( not at all easy) to pass emissions inspection. The stalling has not happened since. I ordered a bosch sensor I think it was around $125.

I am not a mechanic but I like turning wrenches. Some how that sensor replacement sorted it all out. It was the last thing that was done to it on a VERY long list of other trouble shooting replacements including pretty mush everything mentioned in previous replies.

 

Has this P0335 issue been resolved? I have a customer with the issue. I have replaced the sensor but it did NOT help. The car still hesitates while driving and the code has returned.