Back to back showers should be no issue IF your taking a shower to get clean and not to hang out until you are pruned....lol Seriously tho, incoming cold water is a big issue that folks dont think about. Lets say your heater is heating water to 140 degrees ( which is pretty hot!) normal shower temp is more or less give or take 100 degrees and incoming cold water (in wintertime) is 40 degrees If we take your 50 gallon water heater and deplete it by half, now its half full of hot water (140) and half full of cold water (40) which would make the water inside maybe 90 degrees.. which is not as hot as you are calling for in your 100 degree shower. So your 3 gpm showerhead would run out your usable quantity of water pretty quick ( here we base hot /cold water usage in shower at 70% hot 30% cold) With these numbers 3 gpm in 10 minutes would equal 30 gallons, 70% of which is hot. Whats 70% of 30 gallons? 21? So in 10 minutes youre almost down to that halfway point where half the heater is 140 water and half is 40 water.. again 90 degrees.. At 90 degrees in your shower you are probably already cranking the hot valve up a little higher and the cold down a little which is changing the ratio of hot/cold even further making you use even more hot.
Most folks dont have their water heaters turned up to 140 either. More often would be 125 to 130
In the summer when your incoming water is already 75 degrees you barely use any hot to reach the 100 degree mark in the shower PLUS 75 degree and 140 degree water mixed together in your water heater would leave you with 100 degree water for a much longer period of time.
In short, IMHO this is probably a seasonal issue that should clear up when things warm up outside.
yes I do realize that the hot water in the heater rises (toward the outlet) and the cold comes in and is directed to the bottom... but they are still going to mix and lower the overall temperature