How to retain old backups while starting new one

After upgrading to Lion, my Time Machine has developed a problem - I receive the ominous message that TM has verified my backups, finds that it needs to start a new backup, and that this will delete my old backup history.

My TM backup is located on a Time Capsule that also serves as my WiFi router.

I have noticed that I can actually still enter Time Machine and access my old backups. So whatever the 'corruption' of my backup file, it's not so serious as to render my backups completely inaccessible. It would seem a shame, therefore, to have to throw three years of backups away, at least some of which seem to work OK. Nevertheless, I would like to start making new backups again.

What to do?.. I have thought about several options, but I can't get them to work. One idea I had was to delete my most recent backups through the Time Machine interface, because that's probably where something has gone wrong (I may have interrupted the backup process somehow, I have heard that can cause problems). However, this doesn't work; I get the message that I do not have the permissions to do that.

Another option was to simple copy the whole backup to another location, but that does not seem feasible, given the size of the thing. It might take forever to copy that. Also, it seems I need to format the destnation drive in a specific format, which means I cannot use the drive I already had in mind for that purpose. And then I'm not sure TM will be able to access those copied files later on.

So now I'm thinking that I should leave the existing backup alone, maybe rename it somehow, and start a new backup alongside of it on the same drive. If I ever need to access my old backups, I could rename them back to what they were and then access them through TM. This would eman that I would tell my TM that it can start a new backup history, but without it actually deleting my old backups.

Is this possible? Are there better options?