I think it's El Capitan, at least in my case.
I have a Mac mini
Model Name: Mac mini
Model Identifier: Macmini6,2
Processor Name: Intel Core i7
Processor Speed: 2.3 GHz
Number of Processors: 1
Total Number of Cores: 4
L2 Cache (per Core): 256 KB
L3 Cache: 6 MB
Memory: 16 GB
Running
System Version: OS X 10.11.4 (15E65)
Kernel Version: Darwin 15.4.0
My external drive is
Device Name: External HDD
Media Name: Fantom External HDD Media
I have two of the drives mentioned above. Bought at the same time from the same place, both connected via usb, both in place since I purchased the mini. They sit side by side where they have sat for the entire time I've owned them and the computer. Nothing has changed positions, no new cabling, no electrical changes and so on.
External Drive 1 has files on it (1/2 TB give or take)
External Drive 2 is my Time Machine Volume (yes I realize it is the same size as my external drive and could not hold my external drive files plus the mac mini files if both were at capacity)
The drive that gets disconnected from El Capitan is always Drive 1, the drive not functioning in Time Machine capacity. This has only happened since upgrading to the latest version of El Capitan. I was on El Capitan for awhile without issue, but the latest upgrade brought the issue. Presumably the time machine volume has a trickle of OS activity that keeps it online and that accounts for only one of them going missing.
At first I thought my drive might be failing, but if I power it off and back on, it always shows up in the finder. I ran first aid with disk utility, everything is fine.
My conclusion is that it's the OS. Hoping an update takes it away as silently as it appeared.