When I try to open my sites on a shared hosting server in the last few weeks I noticed they were not accessible - at least an hour daily. Apart from server downtime is there a possibility that something is wrong on my end which forbids me to view the sites?
Yes, try to contact your host to know what is happening. Even if the issue is not on their side, I think they will be happy to help you find and resolve it.
An hour of downtime daily is definitely not the routine server downtime that happens. May be just a bad server or it's going over it's limit (ram) often.
Just check with your host and if you can't solve it i'd suggest you move to another host.