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Some copies of the documentation of epsf.tex seemed once to suggest that the command

  \input epsf

is needed for every figure included. If you follow this suggestion too literally, you get an error

  ! No room for a new \read .

after a while; this is because each time epsf.tex is loaded, it allocates itself a new file-reading handle to check the figure for its bounding box, and there just aren’t enough of these things (see no room for a new thing).

The solution is simple — this is in fact an example of misuse of macros; one only need read epsf.tex once, so change

  ...
  \input epsf
  \epsffile{...}
  ...
  \input epsf
  \epsffile{...}

(and so on) with a single

  \input epsf

somewhere near the start of your document, and then decorate your \epsffile statements with no more than adjustments of \epsfxsize and so on.