My thoughts are that ideally you want to be turning a weekly profit that's fairly substantial, and then that's the type of money you'd want to use to improve the arena. I don't think dumping lump sum payouts into it are necessarily a bad thing, of course, but I'd rather either look to make improvements if you think those are needed or park the cash for a little while until you know whether you need improvements or not.
Now that the relegation series start with 5th instead of fourth, my traditional goal of aiming for 5th or higher isn't quite as effective, either. Basically, when you move up, you want to try to ensure that you can at least remain in the league and be profitable at first, and then start progressing until being able to move up another level.
Of course, that's all general stuff. If you know you're demoting, and there's nothing you can do about it, there'd be little point in investing in veterans for this season unless they're guys you can afford to keep after demotion and who can help you win next season and when you return.