There are a lot of assumptions (on my behalf) inferred from the information you have given us.
14 bytes sounds like the default FIFO buffer size for COMn: ports (under win32 anyway).
That you get the first 14 bytes and no more suggests that some form of handshaking is involved. That it isn't being reset automatically means that it (the comm port) is probably set up for software (Xon/Xoff) handshaking.
If you are on a win32 system, the easiest way to verify this would be to open a CMD window and issue the command:
That was from the (currently inactive) com1 on my NT system.
If you are simply reading from the port and want to 'slurp' as much as possible, you could use the control-panel->ports (or the mode command (see help mode) to switch the handshaking off.
This isn't going to help much if the device attached to the other end needs the hadshaking though. If the device is waiting for you to empty the buffer, and has recieved an Xoff (ascii 14?) ... it will be waiting for an Xon (ascii 15?). Maybe just writing the appropriate one will restart the flow. There is probably a module that will take care of this nastiness for you on CPAN.
Of course, if your not using win32, ignore me and wait for one of the "real programmers" to supply similar info for *nix systems:)