Typically, with my Reecom unit, back to back warnings do not silence the radio in between alerts because there is always a three second pause after the final EOM signal is sent before the audio mutes. My unit never instantly responds to the first EOM... it waits for the sequence to complete.
I have run into problems when our local weather radio sends out an EOM the radio doesn't recognize (about 20 percent of the time), leaving the audio on. But I suspect the station more than the radio. When an intern does the Wednesday 11am test, at least half the time they screw up the EOM. Only this time the radio signal goes silent (the Reecom audio is still active though). After about 10 seconds of silence, the transmitter automatically shuts off and apparently recycles, returning to the air after a minute or two, but not before you are treated to the blast of white noise from a dead frequency.
We have four active weather radios here - one in the bedroom (a Radio Shack that does recognize EOM), one in the guest room (a cheapo Midland that does not have an alert tone but merely opens the audio when an alert comes through -- it also recognizes EOM), a newer Midland I use to feed KHA-53 for 24/7 streaming on Weather Underground, which does not recognize EOM but mutes after five minutes, and the Reecom.
Of all of these Reecom is by far the best and I highly recommend them, even though they cost more. Don't bother with the AM/FM unit though -- the audio from the speaker is obviously designed for the limited bandwidth NOAA signal, not broadcast radio. The Reecom's varying audio alert tones which help you distinguish between a test, a watch and a warning are very helpful, the audio is the loudest and clearest of all of my weather radios, and although I wish the radio responded immediately on hearing the first EOM, it's a minor issue for me overall.
My pet peeve are radios that ignore the EOM standard altogether. How hard could it be to program a radio to open the audio during an alert, and mute it when it completes with an EOM signal. A five minute timeout can be a real nuisance if you are in bed, get an alert for a watch and then lay there waiting for the darn thing to mute.