It sounds like the long duration of rain you are describing, with a cell appearing to be on top of you, is an instance where the cell propagation vector was opposite of the cell motion vector. Take a look of the thunderstorm cross-section via the COMET program.
Once a cell initiates, it grows upscale into a mature thunderstorm/cell, then it decays (rains out). Thunderstorms are not usually made of one cell. More often one cell initiates, grows upscale, aids in spawning new cells (such as through cold pool interactions) and the cycle repeats. The motion where the cells are coming from (cell propagation vector) adds a component to the system motion, what you actually appear to see. Often times we largely see thunderstorms move with the same direction as the cell motion vector, the direction mid/upper level winds are pushing the cells. (Notice in the “stationary thunderstorm”, how stratiform rain from decaying cells is moving from southwest to northeast and how the most intense part of the storm appears to be sagging south.) Both vectors, the cell propagation and cell motion vector need to be considered additively if the system motion is to be determined.
In your case, though the thunderstorm, system motion, appears stationary the cells are actually moving but the propagation vector appears to be opposing the cell motion vector. See the useful website for more information
Hope this helped though probably not explained in the best manner possible,
Matt, B.S. Meteorology