This client-side error may be caused by any AJAX component, not only AutoSuggestMenu.
You may find a lot of info, searching Google with keyword "Sys.webforms.pagerequestmanagertimeoutexception"
Here are some of them:
As for ASM concerns, this error may be caused, for example, by too long SQL search, or failure inside GetSuggestions
server-side function, so that no result is returned to the client.
Regards,
Astor