This is something I’ve run into. An IFR planned flight with ample reserves but at max range. In case 1 it was simply a difference between forecast and actual winds. In case 2 it was due to light but undetected icing which slowed me down for a couple of hours of flight.
In case 1 the wind difference became apparent early on. Updated range and endurance estimates were reviewed every 30 mins in synch with tank changes. Though filed IFR, conditions were hard VMC all the way to the destination. So I closely monitored everything and was convinced that I would arrive at the destination with between 5-10 gallons of the 60 I carry. That estimate assumed arrival at cruise altitude (9K) over a 1K airport so there was fudge in there. I would arrive just after dark due to the wind but the FBO would be open (for transportation and hotel help). I had 5 gals when I landed.
Anything under 10 gallons is below my personal mins (IO-540 LOP). That is, I would never plan a flight where I arrive with less than 10 gallons just as I wouldn’t plan a flight with less than IFR reserves. But the reserve is included exactly for such situations and I’ll use part of it in the air if it makes sense to me and doesn’t make my taint quiver (that’s my tell). In recent years wx forecasts and reports have become increasingly accurate and reliable so this kind of thing rarely happens to me any longer. My plane’s instrumentation is accurate and well tested. I have both floats and a flow gauge that I cross check. While the floats are inaccurate with > half full tanks, the last 10 gallons are very accurate. And the flow gauge, after some re-engineering, is accurate to plus/minus 1/2 gallon over the full 60 gallon burn. I have a reliable GPH readout.
Case 2 was the day Hurricane Sandy hit NY.
I was flying from Key West to 8NC8 (KRDU). I can’t recall whether I planned a non-stop or not but I knew it was feasible. The winds from Sandy would slightly benefit the entire flight and I timed it so I would land after it has passed by destination. Arrival would be just after sunset. Took off KEYW in hard VMC but wholly within the influence of Sandy’s low, and off we went. Somewhere over Georgia my speed began to very slightly decay and all the range endurance calculations began to show it. Didn’t know what was happening but monitored it very closely. Conditions were hazy with varying visibility. Over SC it was clear that my personal minimums were going to be cut into if I continued home. But moreover, KRDU was going to be just barely VFR with plenty of clouds and showers to circumvent in the fading light.
About the same time I decided to land at KSOP for fuel I discovered trace amounts of ice on the plane. I concluded that it was the reason for the decayed airspeed ever since we hit the hazy, not quite in cloud, conditions. In any case, the combination of darkness, decaying conditions as we headed north and less than an hour’s fuel left at my final destination told me to land and reassess. No questions.
We did take off after some weather checks, full tanks and some restful thought. The controllers at RDU were ‘were full on’ and when I told them I’d like to land on the grass at 8NC8, they told me, “we’ll get you in there, fly....”. They took me around the cloudy parts and I did the downhill, gusty wind, night time landing to my home ‘port. Very satisfying end to the day and very comfortable with 5+ hours of fuel on board.
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I had to go back and check I was on PoA, LOL. 
