in most instances. It is fairly effortless to acknowledge the receipt of an email, even if you cannot yet confirm your availability. This is basic customer service.
There is cell service or WiFi in most places, making it highly unlikely that the lack of response is truly due to lack of signal.
I respond to emails on weekends and holidays, although I enable an "Out of Office" auto response on long vacations. I will always get around to responding, but this will indicate that it might take more time. It is not unrealistic to expect people in most businesses, including this one, to handle it similarly.
That said, I will typically give a new Introduction/Appointment Request 48 hours before reaching out again. I will then wait 24 hour hours before crossing that person off the list and moving on.
The above timeframe is sufficient for a provider to respond 95% of the time.
To the extent circumstances are such that it was impossible to respond within the requested timeframe, a follow up email saying, "Hey, thanks for your interest, I regret not being able to get back to you in time, I hope we can connect next time" from a provider will likely have me approach that person again.
Honestly, I have been extremely lucky during my years in this game, as the overwhelming number of providers I have approached have been super responsive and accommodating.
el dude