This isn't anything related to avast, which doesn't have a firewall, so I can't see why it would shutdown the windows firewall, even if it had that functionality (the ability to shutdown the firewall, which it doesn't).
What is your OS (XP, Vista, etc.) ?
Do you have any other security software, if so what ?
Do you have another firewall installed ?
So I think it is something different, unrelated to avast, there is some malware that tries to shutdown your protection, e.g. firewall/anti-virus, etc. So it may be worth running an anti-spyware scan.
If you haven't already got this software (freeware), download, install, update and run it, preferably in safe mode.
1. If using winXP or Vista
SUPERantispyware On-Demand only in free version. Or
AVG anti-spyware (formerly Ewido) Resident scanner during trial On-Demand after trial ends. Or
Spyware Terminator Resident scanner.