Embedded breakpoints not always cleared

I'm working on an embedded target using a Segger J-Link debug probe.  One frequent annoying problem I'm running into with CLion, is that it doesn't clear breakpoints from the target if I remove them in the IDE while not connected.

A common use case sequence goes something like this:

1. Set a breakpoint in CLion
2. Click “Debug ‘projectname'”, which downloads the code and runs it on the target with the debugger attached
3. CLion debugger stops at the breakpoint, as it should
4. Disconnect from the target
5. Clear the breakpoint in CLion
6. Click “Debug ‘projectname’” to run the code again
7. CLion debugger stops at the now-nonexistent breakpoint location

I think what's happening is that CLion isn't correctly synchronizing the state of its breakpoints with the debug probe, so that any breakpoints leftover from a previous debug session aren't getting cleared when it reattaches.