Drove or Drive

[spenser]

In the following sentence, should the word in bold be "drove" or "drive"?

The petition demands that the government abandon proposals to establish a national vehicle-tracking system that would be used to tax motorists every time they drove their cars.

[2006]

In the following sentence, should the word in bold be "drove" or "drive"?

The petition demands that the government abandon proposals to establish a national vehicle-tracking system that would be used to tax motorists every time they drove their cars.

I prefer "drive".

[spenser]

When I read the sentence I felt that it should have been "drive" but is there a grammatical reason for the switch to the past tense?

[2006]

When I read the sentence I felt that it should have been "drive" but is there a grammatical reason for the switch to the past tense?

Not as far as I am concerned. I would have used "drive"; I see no reason to prefer "drove".