Or,

(104)Connection reset by peer: mod_fcgid: error reading data from FastCGI server
(104)Connection reset by peer: mod_fcgid: ap_pass_brigade failed in handle_request_ipc function

And

mod_fcgid: read data timeout in 40 seconds

There's not a lot around that is helpful about these errors, so after having to try to sort them out myself, here's a report on what I've found. It's got to be worth telling you, I was up til 1am.

Summary

FcgidBusyTimeout (old name BusyTimeout) is the setting that governs the first error. Set to default and a download initiated by php will timeout after about 450 seconds, giving:

(104)Connection reset by peer: mod_fcgid: error reading data from FastCGI server
(104)Connection reset by peer: mod_fcgid: ap_pass_brigade failed in handle_request_ipc function

I think that "about 450 seconds" is a combination of 300 seconds for the FcgidBusyTimeout setting, and 120 seconds for the FcgidBusyScanInterval, and some fudge time

Only people with slow download speeds / downloading large files will force this error.

FcgidIOTimeout (old name IPCCommTimeout) governs the read data timeout error. A php script that waits for something to happen (like a download to finish) will timeout after 40 seconds when this is at its default setting, giving:

mod_fcgid: read data timeout in 40 seconds
Premature end of script headers: scriptname.php

Solution

FcgidBusyTimeout 3600
# or whatever big number you want
# 3600 (seconds) allows an hour for a download
#
FcgidIOTimeout 600
# or whatever
# 600 seconds allows 10 minutes for a script to wait
# you just need to adjust it to suit the scripts you run

Where?

In this section, in httpd.conf, before the virtual hosts:

<IfModule mod_fcgid.c>
FcgidBusyTimeout 3600
FcgidIOTimeout    600
# other Fcgid directives...
</IfModule>

Alternatively, if you're running CPanel+WHM, use the include editor: Service Config > Apache Config > Include Editor > Pre Virtual Host Include

More Detail

Here's an annotated selection of mod_fcgid settings for httpd.conf:

<IfModule mod_fcgid.c>
# Set a maximum number of requests a process will handle,
# then it'll die
# this is just to keep memory cleaned up
# somewhere I've read that a php process will die after 500,
# whatever you set here
# but you need to set 500 here as well!
    FcgidMaxRequestsPerProcess 500
#
# These two govern how many processes are created, 
# but I'm using defaults so I've commented them out
#   FcgidMaxProcesses            6
#   FcgidMaxProcessesPerClass    6
#
# What's the least number of processes for a class?
# not sure what a 'class' is, but set this zero
# to enable processes to be killed off
    FcgidMinProcessesPerClass    0
#
# Now some idle settings
#
# Scan interval, fairly straight forward – how often it checks 
    FcgidIdleScanInterval       30
#
# How long should a process be idle for before we kill it?
    FcgidIdleTimeout           300
#
# How old do you want processes to get?
# Once they get to this number, they'll be killed once they're 
# idle, regardless of FcgidIdleTimeout
# its another way of doing what FcgidMaxRequestsPerProcess does, 
# but with time instead of requests
    FcgidProcessLifeTime      3600
#
# What about a process waiting for a connection to be made?
    FcgidConnectTimeout        100
#
# And this is a timer for a script that has connected, 
# but is waiting for input/output to happen,
# like a script waiting for an upload
    FcgidIOTimeout             600
#
# a FastCGI application will be killed after handling
# a request for FcgidBusyTimeout
# This is the one that kills long downloads
# - the download is busy, but waiting, so it times-out
    FcgidBusyTimeout          3600
#
# This is self-explanatory, the interval that 'busy' is checked
    FcgidBusyScanInterval      120
#
# And last, but not least, the size of requests that can be made
# needs to be bigger than any upload you want to do
    FcgidMaxRequestLen   100000000
</IfModule>