Serial Monitor odd behavior

Arduino UNO R3. When I first connect to my laptop with a USB cable I get a sound and the Device Manager window shows Ports(COM & LPT)-USB Serial (Communication Class, Abstract Control Model) (COM5). The IDE Tools window show COM3 and COM5 are available and COM5 is checked. If I unplug the USB and reconnect it to reboot the UNO (the UNO is imbedded in my application and I can't reach the Reset button) I get the sound and the Device Manager window shows the same as above but only COM3 is available, hence, I can't use the Serial Monitor. Several tries don't help. If I leave it unplugged for a while it works. What am I doing wrong?

Bob Weber

What am I doing wrong?

The only thing I can see that you are doing wrong is this:

the UNO is imbedded in my application and I can't reach the Reset button

The reset button can be brought to the surface of the enclosure quite easily.

Although, I suspect that that won't help.

I can't use the Serial Monitor.

What does the IDE show?