"cant connect to mysql ....mysql.sock"

Hi evry1
I have a site runnin on redhat linux (www.spolitiche.unimi.it)
Its workin for the past 2 years without interruption, nobody modified or deleted part of installation but, 2 days ago, each few hours the site (php mysql driven) goes crazy and i see error messages like "Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock'"

If i reboot the machine, it works..but few hours later...again errors.
Since nobody touched config..what can be cause? and how can i fix it? ..im not so expert in linux ( sorry for the question !!!
Grazie,
Ivan


ps
can it be a "disk space" problem?
whats the commadn to check for left space in the partitions?

I know..im so newbie sorry (( i feel ashamed