The Auto FTP calculation varies by Garmin model, with the older Garmins having simple estimation that requires steady 20-min efforts. Which Garmin do you have, and what are you using for HR?
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Sure, a couple months ago I did 3 x 2-min at 125%-133% and received an FTP update. And that was not a max effort.
I’ve a 530 and currently using a Polar Verity Sense, but the FTP estimation was equally junk when I was using a Garmin HRM.
Sorry to hear that. Same model as mine, so I’m assuming you either have issues with clean heart rate variability data, or enough steady efforts in order to get a good VO2max estimate. Or you need to update personal information, in particular Activity Level and HRmax and possibly Lactate HR.
I only take post-ride pics of the FTP updates. Looking at Garmin connect my vo2max bumped up from 42 to 43 the week of May 3rd (week of the 17-min climb). And WKO had estimated vo2max absolute go from 3.990 to 4.003 on the 17-min climb. Its easier to see vo2 trends in WKO (and workout level % vo2max), so I mostly ignore the vo2max estimates in Garmin.
And to be fair, I see updates to FTP estimates without vo2max changes.
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I read all the firstbeat stuff and googled and came up empty.
My 530 always wants me to do more high aerobic for optimal training but I think that pleasing the Garmin gods would kill me.
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A little high aerobic goes a long way 
My auto FTP rarely updates.
But it does like to auto update when I do a ramp test, and it is usually pretty close, 5-10 watts of TR. The targeted efforts seem to line up with my efforts as well (I have a MASSIVE base, so that blue bar is pretty long).
Currently my VO2 and FTP seem a little low, but my last few hard efforts were done at 6000’ higher than I live. I’m not going to worry about them though.
WKO puts me at 42.1, Garmin puts me at 43, and that formula underestimates at 36.5. A pretty big gap.
There is a more detailed formula but it requires an estimated efficiency.
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GoldenCheetah uses Critical Power as far as I know from looking at the source code. CP is based on an all-out max effort of 2-3 minutes.
Going back to this formula it has never made sense why Hunter Allen stated that FTP from a 20-min field test be used, as that would seem to tell me VO2 at FTP and not vo2max.
Looking up the ACSM formula it does appear to be VO2 at a certain power. Therefore using a max 5 minute power should provide an estimate close to VO2max. I don’t have a recent 5-min max effort, however I definitely get better results from the ACSM formula using my current 5-min best power.
I don’t know what it could be. I would have thought the Garmin software engineers might have considered adding to their algorithm some code that effectively ensures that FTP will be revised upwards if the individual has completed a 40min+ effort at gt. currently estimated FTP.
On 3 May I completed a continuous 80min sweetspot effort at 283w. HR was ~10bpm below threshold. Today it thinks my FTP is 274w. 
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