Paper based permit system should work without issues like you talked about . It seems like you have a problem with the management side of things . Lack of training in completing permits and contractors should not be allowed to leave site without a system in place to sign of this very important paper work .
I think more information is needed about your place of work Job type etc to further comments .

To add to the advice above I suggest you look at the PTW system itself. I have seen some unbelievably complex PTW systems in the past that seem more intent on trying to prove something in a court of law than doing what they are intended for, which is to act as a record of control of the contractor.

When I train permit issuers on a procedure I stress time and again that the form is not the object of the exercise, it is simply a record to show that you controlled a contractor undertaking a high risk job. The real work is to ensure he has identified and controlled his risks, actually has the identified control measures in place before starting and has coordinated with anyone else in the area to ensure no-one is put at unnecessary risk. If you can get that message across to those issuing the permits then the form becomes easy as it is then a useful record for the controller person to prove that he has done what you have asked of him.

Ask your staff why they have not completed the forms; it may well be that they fail to understand what it is for or they may not actually be the one controlling the contractor.