Handytone 286 Fax Machine issues

Now, please forgive me if this isn't actually a Handytone issue. I have a Trixbox running 2.6.2.3. It has a Sangoma A101DE T1 card, on which we have 8 channels for voice.

Connected to this Trixbox I have an HT286 that is connected to a fax machine. The fax machine is setup through trixbox as a fax machine (I.e. in general setup, the fax is pointed to it's extension. However, I have done no additional configuration of the fax extension, since I treat it like a SIP extension. The fax machine works most of the time. When it doesn't work, I get "comm. error" and it retries and retries and retries until it gives up after the 3rd retry. The fax machine is an HP 3055 All-in-One OfficeJet. The logs from Asterisk show the call connects successfully but ends with a hangup "cause 16".

The weird part is that it only has issues with certain numbers. And that with those numbers, the issues are repeatable over and over again. (I.e. Never able to successfully send a fax to them.) The configuration on my HT286 is default except for the following change. Without this it would not successfully fax anyone. The T.38 auto detection seemed to mess it up:
Fax: Passthrough

All of that being said, I'm sure it's something I've missed, or mis-configured. I guess my question is, why is it working with 85% or so of the faxes we send, but repeatedly failing on certain numbers? Any suggestions would be welcome, if you need more information, please let me know and I'll paste what I can.

*Edit: One of the suggestions given to me locally here at the office is to slow down the baud rate on the fax machine, as it is greater than the sampling rate of the VoIP stream.