I suspect your drill press is not running correctly, as others have said, if the bit is up and just stopping.
If you have a mill press, often the chuck will use a morse taper, #1 or #2. On occasion, this may get a bit rusty, especially if it has been unused for a while. Clean and reseat it. They, the male/female seats, *should* be fairly bright with no oil on them (well, maybe a light rustproofing film.)
This *can* slip even if the motor and pully's are functioning normally. You may need to clean the rust and reseat it. I didn't see where this was mentioned.
Aluminum is a very sticky metal. Often, it will build up around a less than perfectly sharp bit. The heat will actually fuse shavings to the sides of the bit making the bit VERY difficult to penetrate to any depth. The metal will expand with heat, then contract around the bit, rather like a vise. Normally these are both symptoms of a dull bit and/or too high of a turning speed. Slower is often better. Pressure can do this, too. Really a bit of an art.
The first 1/4" may be worn a little and the upper portions are still the correct diameter, also. This has happened with bits that have been resharpened 8-9 times, too. With deeper cuts, you end up cutting a LOT of metal. Old belts sometimes develop a glaze and slip very easily. Take it off and try scrubbing it with some alcohol and a fine wire brush. It might need replacing if it is really bad and has notches in it. It's very hard to regulate speed and pressure with a bad belt/inconsistent belt pressure. Check the tension, while I am thinking about it. Aluminum should cut easily but it has some quirks. Like brass, it will often dimple around a hole slightly anyway. (Brass is not quite as sticky, though.)
Oil, or, cutting fluid (often soda water) will help, but was mentioned.
Not real complicated, the splined shaft should not be dropping below the seat, of course. And the motor should spin. Not much else to go wrong and freeze up.