It's quite common that parsing rules need to be adjusted a couple of times until they work perfectly. This is so because your emails might have a slightly changing format or missing data fields form time to time.
The recommended way of creating an email parsing rule is to search for a fixed position in the text with a text filter (e.g. search for "Name:") and then define the end position with another text-filter.
To have what we call "robust" parsing rules, we recommend you to flip through different email samples when creating the parsing rules. This allows you to instantly validate if your parsing rule works great with all the samples you provided. You can do this by clicking on the button "Change sample" top right on the parsing rule creation form.
Once you save the parsing rule again, the last 300 emails are re-scheduled for parsing. If your emails got parsed again with the updated parsing rules, you should see the correct results if you open one of the emails.
If you want to push this newly parsed email data to another software with webhooks, you need to re-schedule them for dispatching. What you need to do is select the last emails in the list view and choose "Re-Schedule Webhook Dispatching" in the global actions top-right.
If a parsing rule was working great during the set up but fails later, the cause is most probably that the email format changed slightly. This can either be caused by a change in the email template or if you transitioned from manual forwarding to an automated forwarding. The easiest way do fix that is to open the parsing rule editor again and adjust the rules so that they work well with the latest emails.