Apache Linex server timing out

I run several websites (4 wordpress blogs) nothing fancy, 1 gif RAM on the apache linex server. have been told by host it is a traffic problem... 10-12,000 daily visitors, 15-20K pageviews max - although I hope to grow that. Need a server admin to configure from the apache pre-set limits, I think. Server freezes at odd times... 4 AM east coast, noon, almost any time. Was told it averages 50%, then peaks out at 100% and frezes... I do not notice any actual spike at those times. Joe