Is it normal to UPDATE STATISTICS this frequently? I have a stored procedure that processes data from a source table and is executed many times (about 20,000 executions) throughout the day.

I believe it's getting choked up sometimes, due to parameter sniffing and I've been updating statistics on the relevant tables (8 tables) in the procedure to fix this.

When it gets choked up, a backlog of unprocessed data builds up (which I'm able to monitor the count on.) 

Once I update the statistics the backlog is instantly cleared.

I find myself updating statistics about 10 times a day (almost once an hour).
Does this seem normal or is there a bigger issue I should be looking to fix?
There is multiple ways to fix the parameter sniffing issue.  

If you update your statistics 10 times a day and especially if that is causing performance issues, then I would look at other options.  

There is some good chance that the update of the stats is not what's fixing your parameter sniffing issue. The update of the stats causes the plan to be flushed from the cache (which is probably fixing your issue). Flushing only that plan from the cache would probably work as well without having to rebuild the stats ;)    

If I were you, I would take it from the start and find which set of parameters causes SQL to take a bad execution plan. Once you have this, you can then start looking at the way to fix it. 

You could use the QueryStore to fix this, forcing SQL to use always the "good" execution plan for example.  

Sometimes, A good index can also fix parameter sniffing issue (that can cause SQL to build a different execution plan that would be good  for whatever the parameter is)