I totally understand the lost speech message issue as it impacted my system, and I recently found my answer. However, I have no idea why messages from SHM Delay don’t work, but those from BigTalker do. I did not have that issue. Part of the problem may be the ST Cloud is having issues.
You mention you are using LanNouncer, therefore I assume you are using Android devices or Amazon Fire tablets. What I found was the Amazon OS was putting Lannouncer to sleep and I could not stop it.
The solution should also be running the Fully Kiosk Browser, is using the Fully Kiosk Browser Controller for sounds and TTS.
Same basic setup as LanNouner, create a virtual device for each target device, then connect to whatever does the sounds and talking. On my system it never misses a spoken message, because there seems to be a speech queue in Fully, but no queue for sounds.
I hope this helps, because my only other suggestion is to reboot the speech device when things get bad.