Been thinking about this for a while. Obvious theres the mains things like being able to play many genres and good timing etc..i'm thinking on the consistency thing, like consistent hi hat beats erc. Hope this makes sense!
Reliability, punctuality, easy-going but focussed, sight-reading, musical ability and technical ability on the drums.
Reliability and punctuality are often overlooked but will get you a lot more gigs than those that are not so reliable. I was talking recently to a former professional player and he remarked that the reason he got a lot of work wasn't all down to his playing (although that was very decent) but it was also to do with the fact that he was reliable and easy to work with. There may have been 'better' players out there but they were not always reliable.
Sight reading is also absolutely vital. To a high level.
To be honest, there is very little session work around these days. You have to be an absolutely monster player with all of the right attributes to make a good living.
There's a certain, elusive "mojo" you need as a player. If you can slip into any musical situation, make it work, AND make it sound good, you're golden. After that, it's what you need to be a good employee anywhere else--punctuality, good attitude, etc.
But, yeah, gone are the days of making a living as a session player. I only get about 6 calls a year or so. Mostly, people have a drummer or a decent drum track program they already work with.
The reliability factor bothers me. It implies that some session players are not reliable.
You just can't be late for a recording session, it's impossible. You cannot be unreliable and a session player, unless maybe you're Steve Gadd. I can't imagine being late for a session, much less missing it altogether, I just can't. The person who would do such a thing deserves to be moved down to the C list at the very least.
The way I see it, there is a metric ton of drummers out there that can sucessfully pull off any specific studio need...intangible charactaristics and all....
its really luck..which many equate to preperation meeting chance.
Then, if your flavor gets a little favor, you might make a living at it.
Best to look at something more consistant for paying the bills and moving into being a primarily "studio player" if that path opens up...but always keep yourself ready, available and canvasing - something hard to do in the face of years of faded hope trickling away in the cracks of financial need.