Even if your using a Mac or Linux NEVER assume that the cause of a problem is not some kind of malware and/or a virus. Run a full antivirus and anti-malware scan(s).
Are you using wifi to connect to your router, if so the connection may just be happening to drop out at them times.
Are both FF and Chrome on your computer up to date? (Current versions are 12.0 FF on windows, and 19.0.1084.46 m Chrome again on Windows - Mac versions of them might be different for the current versions)
There is a virus currently doing the rounds which specifically blocks access to all search engines in all browsers. Sorry I can't give you any other details, but any up-to-date anti-virus program should find it.
You should also check your hosts file, which is typically in C:\windows\system32\drivers\etc (depending on your Windows version). This is an ordinary text file that you can open in any text editor. If you see any entries relating to Google or other search engines, try deleting them (make a backup of the file first).
I just found my notes on the virus I mentioned in my previous post. Apparantly, it's called "Trojan horse Agent3.WJV". At least, that's the name that AVG reports it as. I can't say for sure that this particular virus is the cause of your problem, but it would be worth investigating.
I have a Mac, so that particular virus won't affect me (assuming it's Windows only). Also, my problem doesn't block me from all search engines - just Google, as far as I know. I did check Chrome and wound up upgrading it. Thanks for all the tips.
Try deleting your cookies and site preference. That is sometimes working when I face this problem. If this is occurring for the virus mention on the upper post then updated KasperSky can find out the virus and delete it.