I am not sure what the attribution is on your eVar, there could be one value carried forward from a previous visit (if you have it set up to expire based on number of days or months).. but no, there is nothing that says a new paid search will trigger a new visit. Adobe Visits timeout after 30 minutes of inactivity, so if someone is actively clicking on your paid search links (and have not left the site for more than 30 minutes), then they will have multiple ids in the same visit.
Let's assume that your eVar26 is set to the default "Visit" expiry (so no carry forward from a previous visit)
- (user clicks on ad A)
- Page 1 (eVar26 set to "A")
- Page 2 (eVar26 maintains value of "A" due to visit level attribution)
- (user does another search, clicks on ad B)
- Page 3 (eVar26 set to "B")
- (user does another search, clicks on ad C)
- Page 4 (eVar26 set to "C")
- etc
All of the above pages, the user was still in an active session, performing multiple searches, and therefore setting the eVar value multiple times within the same visit.