Ive never found them late, and often found them early over thousands and thousands of dollars a year of stuff.
But I am noticing their definition of two-day is changing a bit...
Here is the typical spectrum of what Prime offers. Remember its after midnight, so it IS the 24th of February when I took these screen shots...
First. I could order these by noon on the 24th and get them on the 24th, for free, with prime:
Or, I could order by late in the day on the 24th and still get stuff by the 26th:
But order something on a thursday or Friday, and what often used to be delivered on Saturday or Sunday, will now have a Monday delivery date. Its too early in the week to show an example of that. Still officially two (business) day shipping I guess, but stuff was readily coming multiple times a day on saturday and sunday, which doesnt seem to be as much the case anymore. Amazon labeled vans do come around, as do plain vehicles filled with people driving packages! But I guess the stuff that doesnt come on Saturday/sunday is necessarily shipped by USPS, FEDEX or UPS, so they do not deliver on at least Sunday... I guess its what is in what warehouse and the driver type associated?
But the above level of service works well for a LOT of stuff.