I probably fit into your hobby runner classification - M54, ran 2x/wk in 2014, 5x/2 wks in 2015, and 3x/wk last year, increasing my average from 13 mpw in 2014 to 18 last year. I ran so little because I was pretty sure based on a long history that running much more would've caused injury. At least for me, running some or most of my miles easy has been important to avoid injury, and one fast run a week has been enough that I've improved steadily, reaching 1:32:xx for my goal half last year, which seems like a decent hobby runner result given my age & lack of mileage.
When I ran 2x/wk, most of the year I ran one long easy run, building up to 14 miles as my goal half approached, and one short run @~5k pace, usually of 1.5 miles + warmup/strides/cooldown. The four 10ks I ran before my goal race also gave me some relatively fast running. In the two months before my goal race, I started replacing the short runs with 4x800m intervals or hill repeats.
When I ran 5x/2 wks, my pattern was long-short-moderate-speed (hills or intervals)-moderate with only one day off after the short run (1.5m@~5k pace) and two off after the other runs. The moderate runs were 6 miles at whatever pace felt just a little faster than easy.
When I ran 3x/wk, my two-week cycle was long-easy-speed (hills or 1200m intervals)-moderate-easy-short. The easy runs were 4-6 miles stopping every half mile for a couple of minutes of leg-strengthening or core exercises. Because of the breaks, I usually wound up running them a bit faster than the moderate runs. The short runs were usually 2 miles @~10k pace + warmup/strides/cooldown.
If that seems like too much easy running for you, the FIRST 3-run-a-week program, with a slogan something like "run less, run faster," has a long run, a tempo, and a speed run along with some hard crosstraining each week. A book is available on Amazon. I would be crippled in a month if I tried that, though.
All that said, everything I've read or heard over the years suggests that if you can find/make the time to run more often, you'd improve. This year I'm building a base of around 30mpw on running two out of every three days. I'll see how it goes when I start adding faster running, but my legs seem to be holding up so far.
FWIW, Runner's World forums may have more people than LRC who can/will give you useful comments on running just a few times a week.