I am sorry you didn’t get the endorsement the first time.
To “re-apply” is simply submitting a new application. You will need to pay the fees again and start your stage 1 application on the home office site. There is no time limit as to when you submit a new application.
The good news is that you have gotten 2 different pieces of feedback as regards your first application. Ensure you fix the issues in applying again. This generally means submitting additional evidence around the criteria you did not qualify on the first time.
It is also important that you do not overtly focus on this and then inadvertently not submit enough evidence for the other criteria that you passed the first time.
Please bear in mind that your new application is a new process entirely. Technation will not refer to your old application in processing it.
Wishing you the very best.