Outlook only connects to 4 at a time per server so others to the same server
may time out. It's more of a problem if you have a lot of mail to download
in one of more of the accounts. You can avoid most problems if you set up
different Send/Receive groups so no two accounts on the same server are
checked at the same time, especially if the accounts get a lot of mail. Set
the most important accounts to poll no more often than 8 - 10 min and the
others less often.
Say you have 4 accounts for each of 3 servers. Make 3 or 4 S/R groups and
put one account from each server in each group. Set one to check every 8
min, one every 10 and one every 12, the 4th would be for 14 min. This should
eliminate most problems, even if you put two accounts for one server in each
group.
if you have auto polling set to less than 5 min, try it at 10 - it may fix
your problems without using S/R groups. Outlook gets buggy when it tries to
start an autopoll when the previous one is still checking mail and may just
stop checking mail period.