I think its fairly different on every realm.
I play in Asia, and I sometimes just go and do lots of mephi runs, which can take a up2 five minutes and I might do 40 of these, and never get a realm down. I have only seen 2 realm downs in my life, and both of those were for server maintenance.
It sounds like on US West and US East that it could be if u make around 5 games and each one is open for less than 5 minutes then there is a good chance that u can get a realm down. (as u guys have more players per server capita)
Its due to the extra stress on the servers, (from making games, as each game open stores certain things to the servers memory) u are more likely to expereince realm downs during peak traffic, rather than off peak, and its possible in US West and US East to get realm downs for just muling ( exiting and entering the same game within a minute or so of each other.
I dont believe there is any exact theory - and u could possibly say do 50 pindle runs in 50 mins all up and not get a realm down, or u could do just 3 runs and then get a realm down.
The time down can vary - and appears to be completely random - anywhere from a few minutes to 5 hours. Apparently if you continue to keep trying to log back on, then it will make your 'ban' longer.
If u do get a realm down, log off from the internet, and restart your interent connection, u should get a new IP address assigned and can dodge the realm down.