Printer Bed Doesn't Drop Fast Enough

The title is confusing, I know, just couldn't figure out a better way to say it.

Anyway, I just got the printer this week, and am using Makerbot's software, the problem is the bed can be perfectly set up when the print starts, but on prints with any real height, I have to basically re-level the bed during the print. If I dont, the nozzle will eventually start dragging across the print and making the print look awful.

I've tried prints at 0.1mm and 0.3mm layers with no change in the problem.

It's so bad that if you don't readjust the bed at the end of the print, the filament on your next print will just dangle out of the nozzle.

You have the filament diameter set incorrectly or you do not have enough retraction or it is otherwise over extruding for some reason.

Sounds like classic over-extrusion. Did you calibrate your extruder?