No, they are not re-swabbing positive cases but they only swab their long standing participants every month
As well as your note (which seems very plausible), how does ONS manage to maintain a representative sample in any case, if they exclude any positive case - which they must as we know you can't retest in 90 days, then these people need to be replaced in the survey with similar profile individuals. But finding similar profile individuals who have not already had the virus (so can't be tested) is obviously getting harder and harder.
Controlling to get a representative sample must be getting progressively more difficult - especially with the excluded people almost guaranteed not to have the virus, so the new members are more likely to be positive than the people they've replaced in the sample.
Can't see any discussion on how they control for that - it wouldn't've made any difference at the start of course, but now...