Decided to test this SRH805S wide band antenna. They claim it covers 144/430/1200 MHz.
While the nano doesn't cover 1200 MHz, it does handle the lower two bands.
Clearly there is a problem as 144 MHz band is not showing any reasonable SWR.
By the way, my graph shows the SWR (left scale in red) and reflected power in percent (right scale in green).
As for the SRH805S, I must have gotten a bad one. One band missing!