After the toilet in the basement has been flushed it burps air like there is an air pocket stuck and it can't realease until it has been refiled?

The most common cause of that is something partially blocking the drain... lodged in the bend in your toilet

1. Plunge good and flush... and repeat, using a good plunger like this:
http://images.google.com/url?q=http:...l/plngrbaf.jpg

2. If that does not take care of it, you snake it out with one of these; a "closet auger":
http://www.sajetting.co.za/springmac...ics/pic005.jpg

They're $30 at HomeDepot. This is your first step - and would be a plumber's first step, too... so save yourself the $50-$75 trip charge for a plumber and try this first step yourself.

Let us know how it goes.

This can also be caused by a clogged vent line for the toilet. You would probably need a plumber for this.