Access is a desktop database and never designed for a website backend, and now MS have the free SQL Server Express for website database backends they seem to be slowly phasing out support for Access, which has allot of limitations and places allot of strain on web servers.
The point as which Access fails with an application like a forum which places allot of strain on the database can be at any point there is no definitive answer. It could be in the first 5 minutes, it could be in the first 5 years.
You should really look at SQL Server from the outset.
If you your present host charges allot for SQL Server which is why you want to use Access, then you may want to look at our own Hosting packages which include SQL Server starting from just £4.99 per month. They also include a free license for Web Wiz Forums Premium Edition Brand-Free saving you a further $249.99. We also carry out the installation and can upgrade the forum for you all in for the £4.99 per month price.
For more info see:-
www.webwiz.net/webhosting