I don't ever experience these problems people report drilling holes in tool steel. It is just not that friggen bad folks. It's annealed! Drill the hole!
I think there are probably three things going on here:
1: letting the bit get really hot, then possibly shocking it with coolant. Flood coolant really helps, but otherwise wet the area and peck frequently enough to let coolant into the cut before the cutter gets too hot.
2: work hardening. Lean into that bit, show it no mercy! Just let off some as the web exits so you don't over feed and ruin the corners. Many steels we work with will work harden if the bit isn't fed hard enough to cut. Also, there are carbides suspended in the steel that you need to get through. If you let it rub, those carbides will dull your bit.
3: play or flexibility in your setup can allow uneven chip loads or chatter as things move around. That will dull a bit.
Cobalt HSS bits do last longer in abrasive applications, and steel with carbides in it are abrasive. I've never done a measured test, but I would expect an American HSS drill bit to drill a few hundred holes in 1/8" D2 before giving up and cobalt HSS perhaps 50% more. Any drill you're likely to come across should be up to the task of drilling a few holes in spheroid annealed steel without problem. Using an appropriate spindle speed, feed and coolant, most any bit should work. Lubrication should be unnecessary in such a shallow hole, but certainly won't hurt.
Larger holes can be done with hole saws. It can also be done with a trepanning cutter. I use circular interpolation...
