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I think the pattern indicates, fairly clearly, that your Garmin 7610 has a problem in its tuner circuitry, perhaps. The problem first showed up with the built-in antenna, but now has affected the external antenna also.
One thing that might make even a replacement fail also, would be poorly regulated supplied voltage to the Garmin unit. That may be consideration for the future.
But, given that the Garmin unit is probably where the problem is, by now if not necessarily originally... then if it is still less than a year old, sending it to Garmin before the 1-year warranty expires, for free covered-by-warranty repairs, might be the best thing to do.
What do you think? let me know, by using the Reply To Expert function, please.