Provided you meet any internal progression criteria, there's no reason you wouldn't. It's possible if you're underperforming in a subject they may ask you to "drop" that one, or change to another. Similarly if you're doing very poorly across the board they may ask you to change to another programme (such as a BTEC or start a new set of A-levels in "different" areas - such as STEM subjects to essay/other subjects and vice versa) or withdraw from that 6th form/college/school.
You don't normally need to "reapply" to continue - it would be an unusual quirk of the provider themself if you did, not a requirement of the actual qualifications.