Google shows this question asked hundreds of times. There are many work-arounds and bug reports on this.
However it isn't a bug. It's a feature. The feature is intended to truncate unwanted signatures from Usenet (forum) posts. The signature is signified by a double hyphen and a space on a line by itself "-- ".
You can turn this feature off in Thunderbird's configuration by:
Advance -> Config Editor -> [I'll be careful] -> (search for)
mail.strip_sig_on_reply -> [toggle it to false].
By the way, I spend about an hour searching for how to do this on every Thunderbird install. Hopefully this definitive answer will save Thunderbird users time.