Especially with automated tests, I would see a great benefit to eliminating the idea of open vs closed runs. The automated builds obviously needs to close runs as the way of closing out work. But this causes the issue of not being able to go back in and supplement a fail result with a defect id and you know an automated test does not create defects as it requires some human interaction.
Thus asking for a project setting where amongst 100s of runs are always available to go in to modify certain fields after the run is finished. Ok, you could close runs but allow certain fields to be read/write per some permission? You might be able to come up with a list of fields that should always be modifiable regardless of the run being open or closed, such as tagging or editing the test run description after a massive failure.
Simply we are missing the ability to edit a run or augment a result with additional information after the automated run. I was thinking of the option to automatically close runs on a nightly basis but that messes up all the time stamps!
I see a potential for adding a re-open existing run, edit run, and re-close run manually, but that would be so tedious and mess with time stamps so please be careful to evaluate a solution. Another idea is to just skip the step of closing runs altogether, but the UI is not optimized or designed for this. This would also lead to a question of having user read/edit privileges control at the project level.