No, they will not unbind just sitting there.
To bind your system together, you need to put the TM1000 and receiver into bind at the same time. The easy way to do this is to use a servo Y lead between the TM1000 and receiver, and put a bind plug in the spare port of the Y. Then power up as normal. You need to see fast blinking on the receiver, all its remote receivers, and the TM1000.
Then you put the transmitter into bind. You will see all the aircraft side pause blinking, blink slowly, and then go on solid.
The DSMX tells you how the transmitter was last bound. That doesn't mean it was last bound to this receiver.
Andy