Edit: According to Rinnai, the minimum flow rate is 0.26 GPM.
I just replaced an old water heater tank with a Rinnai RU199 tankless unit. A dedicated 1/2 return line was ran through the attic to the master shower; the RU199 specifies a "compatible" pump to have recirulation work, so I used a Grundfos GTK15 pump. This pump is meant to be used with 3/4 pipe, but the 3/4 lines are under a slab, and breaking concrete isn't doable, so 1/2 PEX was used.
The unit is throwing a code 63, indicating low flow on the recirculation line. The GTK15 has a head height of 17 feet, which I suspect isn't enough. I had planned on getting a "non-compatible" pump with a higher head height; the RU199 PCB has a header that powers the GTK15's pump, so I'm sure I could either splice a connector for that header, or run a relay, which should work just like the GTK15. The pump I'm looking at has a head height of 30 feet.
Below is a rough diagram of the current piping:
While this may work, I'm sure variables like friction loss factor into this - I'm just not sure which variables I should be looking at when it comes to sizing the pump correctly.