DaanW, I'm completely baffled by the problem you are having. I've never seen a chuck let go of a drill bit like that, unless somebody simply forgot to tighten it on the drill bit. I don't mean to be insulting, but are you tightening the chuck on the drill bit? You are supposed to hold the upper knurled collar still with your left hand, and turn the chuck body to the right with your right hand. Tighten it as much as you can with your hand strength. It doesn't take very much torque to cause it to self-lock, but you aren't going to be able to harm it by over-tightening by hand.
The only other way that I can think of that a chuck wouldn't lock up, is if there are some long metal shaving spirals or wood splinters jammed up inside it, between the jaws. Is the chuck clean inside?
Albrecht's keyless drill chucks are arguably the finest drill chucks made in the world. They are beautifully made and expensive and highly preferred by machinists everywhere. I have several of them, which I mostly use in the tailstocks of my larger metal lathes. I also have one that I use in my mill/drill machine. They are simple and tough and a joy to use.
In my shop, I have about 22 or so drill presses of various sizes, from little tabletop models to big 1200 lb. monsters. Many of those are antiques in storage and under restoration. By quick mental count, I have 10 drill presses which are fully operational and in regular use. Three are in the woodworking shop and seven in the metal shop. Different sizes and setups. Of those 10, three have import 1/2" keyless chucks, the rest are keyed Jacobs chucks. The two drill presses that I use most often, one in the wood shop and one in the metal shop, have the keyless chucks. I really like the speed and convenience of the keyless chucks for drills up to 3/8" shank. That includes most of my woodworking bradpoint bits.
The imported 1/2" keyless chucks are available these days for about $25, and in my experience, they work very well. I have one that has about 25 years of use, and it still hasn't worn out or given me any trouble. The others get used every single day, changing bits multiple times. The imports aren't quite as accurate as an Albrecht, but they are fine for drill press use.
Keyed chucks have more grip for larger woodworking bits like Forstner bits with 1/2" shanks. Most large size bits will have three flats on the 1/2" shank, which helps a lot with the grip in the chuck, either keyed or keyless.
In the metalworking shop, I use the drill press with the keyless chuck for most drills up to 3/8". I use a larger (and slower) drill press with a keyed chuck for straight drills up to 3/4" and for S & D (reduced shank) drills up to 1". Larger than that, in metal, I use Morse Taper style drills, MT3 and MT4.
