Update checks can be turned off since 7.6
Fr an older version, on Windows, you can tweak the Registry to temporarily disable update checks.
Open up registry editor by clicking on the windows search, and typing regedit, click the registry editor to open.
Then in the registry editor go to Computer\HKEY_CURRENT_USER\Software\Resolume B.V.\Resolume Avenue\WinSparkle
(or Arena in the path if you use Arena)
Double click on LastCheckTime (which is the unix time of the last check), and add a 0 to the end of the number you see, and hit OK. With this, Resolume won't check for updates till the year 2475
If You'd like to check for updates, you can then do that in the Avenue (Arena) menu manually, but this will update the check time, so you'd need to repeat the above steps to disable auto check again