Hi.
How big are these logs?
If they aren't that big, 1440 records per day isn't all that much.
Two years of that would be just over a million records, right?
Do you have the space to store that?
If not, you could simply set up a second server and have that take over once the first is out of space. Depending on the software you use to populate the database, this could be as simple as swapping out the IP addresses.
You could also set up something more flexible. Like say, alternating between databases or tables, backing up and clearing the once not in use.
You could even try setting up something using replication, but that might be a bit to much.
(See MySQL :: MySQL 5.0 Reference Manual :: 16 Replication)
Depends on what you need.