Fractional pilot reported brake malfunction prior to the aircraft being towed. Pilot contacted maintenance and made a logbook entry. Upon reviewing the logbook later; pilot found the entry was no longer there and the brake malfunction was still present.

Narrative

The First Officer was the first crewmember to show and because the rest of the crew was delayed due to traffic accidents along their way; the FO started to preflight the plane to minimize the delay. At some point; a line guy came to the plane with a tug and said he needed to move the plane because we were not allowed to launch from that spot. Gear pins were reinstalled; the FO got back in the plane; closed the door; waited for the line guy to confirm the chocks were set and then released the parking brake. Then the line guy indicated the brakes were still set; which the FO insisted and verified the handle was in the off position. The line guy still couldn't move the plane so the FO observed the inboard and outboard brakes were holding pressure in. The FO turned off the HYD pumps and had to pump the brakes manually to bleed off the residual pressure since the pressure wasn't being released by itself. After the plane was relocated and the parking brake was set; it was observed that the parking brake handle was difficult to operate; it felt stiff and difficult to get full travel. When the Captain arrived; the situation was explained to him and both crewmembers agreed to contact Maintenance and get them involved diagnosing the problem. After calling Maintenance and explaining the situation; the Maintenance Controller suggested that it could be a hydraulic check valve issue and the plane should be AOG under parking brake. Write up as follows:'Parking Brake: When FBO came to tow the aircraft The parking brake would not release. The parking brake on message would disappear with brake handle position but the brakes would not release pressure. FO was able to release pressure by selecting Hydraulic 3A off and pumping brake pedals releasing 30-50 psi per pump. Also parking brake handle requires excessive force to operate'.After submitting the write up for Aircraft X on Day 0 we were given a Report brief for Aircraft Y and the logbook disappeared on our brief for Aircraft X. It was determined that previous crew and tail needed to continue to ZZZ and we were reassigned Aircraft X again but now the writeup we had entered an hour ago was not there. It wasn't cleared; it was just gone. Prior to be assigned Aircraft Y we received an invalid flight release notification on Aircraft X due to our AOG status. Not too long after our release for Aircraft X was invalid; but now the open discrepancy was gone and it showed (0) open discrepancies. We also checked the closed discrepancies and there was no record of our submitted discrepancy. We checked to see if it had been entered in error under the wrong tail. It was gone. Then the phone rang and it was Maintenance wanting to know why they had not received the AOG squawk. The next day we return to the aircraft and find that although the parking brake handle had been adjusted and worked much better but the inboard and outboard brake pressures in the hydraulic synoptic page was still pressurizing and holding pressure without the brakes being applied or set. It was also reported that the plane was unusually hard to tow. We had observed about 2000 psi on the brakes pressures even though the brakes were off. It appeared the brakes were partially applied. We called Maintenance and were advised to AOG the plane once again. Repeat write up.Additionally; while on our way to the hotel; there was a phone call from Maintenance to make sure they understood what the problem was and we were on speaker with Person A from Maintenance; who suggested we could just add more power to make the plane move if the brakes were dragging. This felt like our integrity as crew members was in question and safety oriented practices were being disregarded. What does a dragging brake do to our performance? Was he suggesting to just fly the plane in this condition?The next day we were removed from that tail number and assigned a new tail. The airplane was returned to service stating our writeup described normal operation ofthe system. There is language in the Manual that was similar to what we described and mentioned in the sign off but does not explain why the brakes were pressurizing without asking for braking or parking brake nor the brakes being stuck full on brake or partially brake on more than once.