Yesterday I happened to notice this message in the windows event viewer:

The Mozilla Maintenance Service service terminated with the following error:
Incorrect function.

This was an Error-level report. No other indication that anything was busted though.

I don't have access to that machine for a few weeks, so I probably won't be able to help with more digging.

At work we are facing the same error with Firefox 68 ESR. We use Win 8.1 x64 with limited user accounts. The update process was working with the previous ESR version - limited users where able to install updates of Firefox (installed under %ProgramFiles%) automatically. But this does not work anymore since ESR version 68.0 and we had to disable the automatic updates as they where constantly failing.

I found an entry about event id 7023 in the Windows event log.

- <Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event"> 
- <System> 
<Provider Name="Service Control Manager" Guid="{555908d1-a6d7-4695-8e1e-26931d2012f4}" EventSourceName="Service Control Manager" /> 
<EventID Qualifiers="49152">7023</EventID> 
<Version>0</Version> 
<Level>2</Level> 
<Task>0</Task> 
<Opcode>0</Opcode> 
<Keywords>0x8080000000000000</Keywords> 
<TimeCreated SystemTime="2019-09-19T14:47:42.616010900Z" /> 
<EventRecordID>22490</EventRecordID> 
<Correlation /> 
<Execution ProcessID="512" ThreadID="812" /> 
<Channel>System</Channel> 
<Computer>XXXXX</Computer> 
<Security /> 
</System> 
- <EventData> 
<Data Name="param1">Mozilla Maintenance Service</Data> 
<Data Name="param2">%%1</Data> 
<Binary>4D006F007A0069006C006C0061004D00610069006E00740065006E0061006E00630065000000</Binary> 
</EventData> 
</Event>

Clearing priority so this will get attention