It is now obvious that the CTCSS decoders are dropping out due to the loss of received CTCSS tone during the period that the HTX-404 is over deviated.   A similar CTCSS decoder in the IRLP link radio reacts the same way as the repeater CTCSS decoder does.   Several amateur transceivers tolerated the HTX-404 signal much better, but also occasionally drop out.   The repeater and link radio CTCSS decoders could be possibly modified to accept longer CTCSS signal drop outs, but that would lead to unacceptably long system turn around times.

The problem with the HTX-404 is in its design.   The DTMF encoder I.C. signal output pin is normally biased at 0 volts.   While a DTMF tone is being generated this pin is biased at approximately 2.5 volts. The sudden shift to and from 2.5 volts, which is transferred through the audio circuitry via coupling capacitors before being applied to the varactor VCO diodes, creates the wide VCO frequency swings.   This is a poor design that a few cents of components could have corrected.   I tried to come up with a practical solution for the problem, but with SMT construction and limited space in the handheld, any solution would have been messy and require a lot of time and patience to install.

I also found that the tiny push-button PTT switch, on the HTX-404 I tested, generated noise on the transmitted signal if not held very still.   This switch should not have been creating any problems as the radio was nearly new.   Again, a few additional components in the design could have eliminated this problem.   This switch noise problem also affects the radio in exactly the same way as the DTMF encoder does.   And since the noise pulses occur much more rapidly then DTMF digits would ever be sent, much more of the transmitted CTCSS signal is lost and even the more tolerant radios that I tested, when utilizing CTCSS squelch, had a hard time receiving any audio from the HTX-404.

CONCLUSION:
DO NOT PURCHASE A RADIO SHACK HTX-404
IF YOU NEED OR EVER PLAN TO USE CTCSS ENCODING.

Otherwise, I liked the radio. It is solidly built and I would even buy one if:
I needed a UHF handheld,
the price was right,
and
I had NO NEED for CTCSS.