The way I understand it the time dilation refers to what the observer can see, so that matter will fall in but it is just so dilated (from the observational point of view) that it looks like nothing is falling in (the even horizon will be effectively masked by the time dilation and red-shift).
If you were actually there (and you could actually survive it without being stretched into oblivion) then I think the time would feel (to you) like it was passing normally.
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