Actually, if you will analyze the ending, it's already done. It may seem like two transmissions happened but I think there are actually more transmissions. This is purely based on my opinion so I'm not saying that this is right but it could be.
First transmission- it wasn't shown but remember when Lee Jae Han first sent the transmission? Park Hae Young told him to go to that old hospital but Hae Young can't remember him and Jae Han died. That means that they failed on it so he told Hae Young to convince him on 1989 because he knows that the transmission will happen again.
Second transmission- this time, they changed what happened to the first one, that's why Park Hae Young knew that the past has changed when he was being brought to the hospital. He knows that there was first transmission. But they failed again. I think Jae Han died when he was discovered from that car and by that time, Kim Bum Joo might have been alive.
Third transmission- it wasn't shown too but this time they may be able to save Jae Han from dying and Kim Bum Joo died instead of him. They knew that they will never be able to change the past. They worked on it for 15 years, but I guess cold cases weren't left anymore. They could've changed some of those. This time, Jae Han could've died on the future, February 5. So this means Hae Young still has the walkie talkie until February 5, 2015.
Fourth transmission- this time, they were able to solve everything. Jae Han knew that they will be able to catch the real culprit in the future (2015) so he hid in that hospital. No more cold cases, because I guess they never gave up on it on the third transmission so the only thing left is the real case. Jae Han hid in that hospital for 15 years. He waited because he knew that would be the right time to end everything. Remember in the 2nd transmission, he was warned not to go in that old hospital but he went anyway with his team. He used that method to Hae Young and Detective Cha by warning them so that could mean that the two also brought back up with them. Since he did not die anymore, Hae Young doesn't have the walkie talkie but I guess they have a new way of communication. How could Jae Han knows Cha Soo Hyun's number? That could've happened on the third transmission!
The confusing part is the lighting of walkie talkie again. Remember when they prevented him from dying during the second transmission? His walkie talkie lighted up again but there was no transmission to Hae Young and then he was saved. If you will connect it, he could've died (like I said on the third transmission) on February 5 again (since it lighted up) but there was no transmission to Hae Young so they were able to prevent it during the fourth. So that means they were able to save him that day when those guys went to Jae Han. Idk if I made it clear hahaha but they ended it.