It might depend on how you use a database though. As long the fields on which you search are indexed, then access will be able to find the records you need efficiently.
however, if you try to retrieve data, based on some data that cannot be indexed (eg - something that needs to examine each row to determine whether you need the row or not) - then you will definitely notice a slowing down of data retrieval.
So maybe you need to look at archiving some of the transactions, or maybe collapsing some into a more compact analysis system.
The other thing is in general terms, a "big" system needs to be operated differently to a "small to medium system".
eg - take a sales ledger/accounts receivable.
With a small company you are likely to print out and examine the whole ledger.
However, in a large enterprise with hundreds of thousands or even millions of accounts - you just cannot deal with it in that way. Instead,you have to use statistical techniques, and manage by examining exceptions - so your app will need to be designed differently, with considerations like that in mind.
You may even get to a point where calculating things on the fly every time becomes inefficient - and then you have to think about breaking the "cardinal" database rule not to store calculated figures.