What timing. I actually spent a good amount of last night contemplating this very question as I tried to fall asleep. I was approaching it from a slightly different angle - how much karma would an elf or other immortal (vampire, etc.) accumulate over 50 years, 100 years, etc. - but the premise is the same.
Approach 1
The life modules imply that you usually start your career between ages 21-25. The average starting point of a career is between 750 (life modules) and 800 karma (point buy), which suggests that the average proto-runner is earning 2.5 karma per month over the first couple decades of their life.
Pros: Simple, straightforward.
Cons: The steep growth curve of early life, especially physical maturity, eventually flattens out. In other words, this rate of progress might not be sustainable.
Approach 2
Let's break down a component of the life modules with known durations. State College (65 karma), Ivy League University (85 karma), and Military Academy (115 karma) all take four years theoretically. Some of the differences in karma cost can be attributed to intensity and rigor, similar to Sphinx's rule of thumb. These values imply a range of 1.4 to 2.4 karma per month, presuming 48 months total (and ignoring the Tommy Boy approach to post-secondary education).
Pros: More scalable than Approach 1, and more granular as well (examining 4 years of growth at a time rather than 20+ years as a whole).
Cons: Not entirely consistent with other life modules. Community college, a 2-year program, costs 55 karma, which equates to 2.3 per month, making community college more rigorous than an Ivy League University. This approach also equates the karma-spending rate with the karma-earning rate, which may not be accurate since characters leave the life modules with leftover karma to spend (implying that they store/save some up along the way).
Approach 3
Let's use the training tables on p. 107 of SR5 and compare the amount of time to learn a skill versus the karma to learn said skill. It takes 780 days and 156 karma to train a skill from 0 to 12. (This ignores training bonuses/reductions from various Lifestyle improvements, like a firing range.) 780 days is 156 five-day work weeks. That suggests 1 karma per week, or 4 to 4.35 karma per month.
Pros: We have a direct comparison between karma spent and skill development time.
Cons: This values is very high, and approach produces even higher (and more nonsensical values) at lower skill ratings. Similar to approach #2, this approach also suffers from the assumption that karma is spent at the same rate it is earned, instead of assuming that some of the karma was accumulated prior to training.
For all that, I'm not sure I came up with anything better than Sphinx's rule of thumb. I finally settled on 2.5 karma per month for the character in question, figuring that it would represent a reasonable balance for a long shadow career largely composed of productive routine but occasionally punctuated by explosions and hit squads.