And there's a reason you can't modify it after closing. You have your Problem and all related tasks to resolve the Problem. You test it and if it's really resolved, you close it. 

Checking on the response time of a transaction in an appliction (your example) is something that should be part of the application's life cycle. You could create a task when closing a Problem on the CI, but I would relate that task to the CI and not to the Problem. And since this is not an OOB solution, you will need some customization (and with that you can design your own process). 

If my answer helped you in any way, please then mark it as helpful. If it resolved the issue, please mark it as correct.

Mark