Yup, I've got the debug section on the page re-rendering, so I can spot the values dropping out on re-render.

Here is the method that's called to populate the list options:

public list<selectOption> transactionHistoryProductOptions;
        
        public list<SelectOption> getTransactionHistoryProductOptions(){
            system.debug('GETTING THE OPTIONS');
            system.debug('THE OPTIONS ARE - '+transactionHistoryProductOptions);
            if(transactionHistoryProductOptions == null){
	            list<selectOption> transactionHistoryProductOptions = new list<selectOption>();
	            
	            ******
                     IN THIS SECTION THE CODE LOOKS AT ALL OF THE PRODUCTS THAT HAVE BEEN INVOLVED IN TRANSACTIONS IN THE LAST N DAYS (WHERE N IS SET BY THE USER). CODE THEN TURNS THOSE INTO A SET (SO THAT EACH PRODUCT IS ONLY REPRESENTED ONCE) AND THEN A LIST, SO IT CAN BE SORTED BY PRODUCT NAME IN ALPHABETICAL ORDER. THE CODE THEN ENDS UP WITH A LIST (CALLED "BLAH") OF STRINGS WHERE THE FORMAT IS "{!ProductName}HEREISTHEID{!ProductId}
                     ******
	            
	            for(string s : blah){
	            	list<string> blahlist = s.split('HEREISTHEID');
	            	transactionHistoryProductOptions.add(new selectOption(blahlist[1],blahlist[0]));
	            	system.debug('HERE IS THE LIST SO FAR: '+transactionHistoryProductOptions);
	            }
	            
	            system.debug('HERE IS THE LIST OF OPTIONS NOW = '+transactionHistoryProductOptions);
            }
				            
	   system.debug('HERE IS THE LIST OF OPTIONS - '+transactionHistoryProductOptions);
	   return transactionHistoryProductOptions;
            
        }

 In the debug log, the debug statements can see the transactionHistoryProductOptions list being assembled. Then, as the code leaves the "If" statement, the list apparently goes to null again before being returned.

I've also tried putting the return statement within the if statement and made it an "if-else" statement so that the list is either populated and returned, or just returned as-is. In this instance, the old problem returns of certain values being "dropped" when the user hits submit, even though the list should remain unchanged.