Jet can be a very good data store for any number of desktop development platforms, not just with Access itself. It's always been a first choice for VB developers and still is (for good reason).
A 1GB MDB that is not expected to grow a lot ought not be a problem in terms of speed or reliability. If it's slow, then you haven't indexed it right, or you're writing very inefficient SQL. An example of inefficient SQL would be applying WHERE clauses to expressions, which therefore can't use indexes -- an example would be
WHERE Year([MyTable].[MyDate]) = 2002
as opposed to
WHERE MyTable.MyDate Between #1/1/2002# And #12/31/2002#
If you're having stability issues (i.e., recurrent corruption), that's a problem that needs to be addressed -- it's usually due to human error, hardware problems or software issues (like AV software interfering with internal Jet write operations).
But the key determinant is how fast the MDB is growing. If you extrapolate out the historical growth rate and approach 2GBs within 5 years, I'd say you need to upsize soon. If it's more like 10 years, you should probably do it anyway. If it's 20 years, then, not so much.