Hi Barry, I asked pretty much the exact same question below this post, so you should find some answers there. In terms of punctuality I'm not sure but as far as my research has gone most of these trains are extremely punctual indeed, but of course no one can ever guarantee a train will be on time.
As far as other posters have commented, buying the tickets for just one day in advance should be fine, I will be doing this myself on around January 10th in Irkutsk and then Ulan-Bator. The only thing I have not found out yet is if they will be more expensive buying just one day before?? So if you find this out let me know…
Well, the price should not change with the dates closing. If you want I can check it at the station next time I go there.
Another option I might do is buy the ticket from Russia into Mongolia at a Moscow station when I arrive in Moscow, as I am sure you can do this there.
I met quite a few people who wanted to change the date of departure for different reasons (schedule shift, they liked russia and many more). But they couldn't because you can do it only at the international counter where you bought it. Some took the train anyways, some lost money. Decide for yourself.
I don't remember if I told you this already. The train from Irkutsk to Ulan-Bator departs at 9pm and arrives 6am 2 days later. So it takes about 33 hours, most of which you spend on the border (10-12 hours). Toilets locked up, but you can go to the station toilet. The price should be about 4000-5000 roubles as far as I remember. Am I right?
Alternative is to take train from Irk to Ulan-Ude (about 900 roubles 3rd class), takes 7 hours, departs at 9pm, arrives at 7am. Spend a night in Ulan-Ude (like 500r) seeing the stuff, take international bus, takes 10 hours, departs at 7.30am, arrives 6pm, price is 1600-1700 roubles.