Method 1: I would suggest you to first check if the services associated with system restore are working.
Check for the service Volume Shadow Copy if it is running or not. To check for the services –
Go to Start - Run and type Services.msc then press enter.
Under the Status column look for any entries that read as "Started".
And check if the service is set to automatic or manual.
Note: If the service is stopped, all the Restore points will be deleted.
Method 2: You may boot in safe mode and then try to perform a system restore. This will help check if any non-Microsoft service is interfering with the system restore.