Avast needs only one reboot when installing. Constantly rebooting can mean several things
1) Something went wrong during the installation. Remove Avast, reboot and try again. Make sure the installer isn't corrupted. Download Avast again in another folder and compare the two installers.
2) A application is interfering with Avast. Remove all applications from the startup list using msconfig or startup.cpl, reboot and try again.
3) There is something wrong with your operating system (registry?). Try a in-place repair of the OS.
There may ofcourse be other reasons, but these come up in my mind.