There are 23 possible different 744's that UA uses -- any of which could on this schedule (and no they don't use the same aircraft on the same route on a regular basis). Unless you can provide the tail number of the flight you were on, no way to tell if the same aircraft is being used or no. Plus the likelihood of any FT having recent knowledge of that particular seat is next to zero.
However, it is unlikely a seat would go unrepaired for a week or more.