This issue was previously reported here: MacOS Sierra; Text deselecting when using scroll-wheel with Logitech mouse., but there is not a solution, the question is a year and a half old, and the issue is closed without higher rep.
Text selection stops and restarts when using a mouse wheel. This problem does not occur when using the trackpad.
The issue is not Logitech specific--I use a Kensington trackball and work and a Logitech trackball at home, and I have the same problem with both.
The posted select-scroll-shift-select solution works, but is frustrating.