Nano will not connect via UART with serial device unless USB is present

I am using an Arduino Nano clone with the SoftwareSerial library to communicate via UART with a third party serial device. In the board, I have 5 V that power up both the Nano and the serial device. The serial device has a removable internal battery pack and it is prepared to work without the battery pack as long as it is connected to the the external 5 V power supply. I have been able to operate without the battery pack in the serial device as long as I have the 5V power supply present AND the Nano connected to a computer, through its USB. If I remove the USB cable to the computer the serial connection between the Nano and the serial device does not occur. I have tried different possible solutions such as powering up the USB connector without the computer connected, different Arduinos, different serial devices, etc. always with the same result. I get it to work when:

a) I have 5V, internal battery, USB connection
b) 5 V and internal battery
c) 5 V and USB connection to computer

but I can’t get it to work with the 5 V alone, as it is supposed to do. Any help will be greatly appreciated.

Just a wild guess (no enough information supplied to make a more elaborated guess): The ominous "serial device" needs a bit more than 5V to operate correctly. The 6V battery provides that, most USB ports on PCs have a bit more than 5V but your voltage regulator is a bit below that. Take a multimeter and check the voltage on the 5V pin if the USB is connected and if it isn't connected. If it's slightly higher in the first case, I would check this.

Plug in the battery and measure the voltage on the + - lines to see what voltage your battery is providing. Batteries lose their ability to provide the rated voltage over time. Measuring it under load enables you to see how much it's sagging. It's probably dropping below the required voltage needed to run the component. Or worst case, you have a short.