I don't get it. Why would they hang up?
Many times because:
a) They mistake the "Relay service" as a service that "Sells something" (ie like carpet cleaning, insurance, cruises etc) or think it's a charity asking for money... they don't understand that it's a translation service and hang up saying "sorry we don't want any", or "we've already donated to ...."
b) They've been "burned" too many times by scammers who use relay as a means to commit a fraud/scam from various places including prisons and foreign countries - Nigeria being the location of most scam calls for the last 10+years.
While it's very frustrating - I try to remember that many people have never even heard of a "Relay service" let alone USED one to have a conversation with someone. If I'm going to be doing a transaction , or starting a long term relationship with a company etc I always try to email that place first and make a contact with a specific person (for example "Jim" at my car dealership/repair centre). In the emails I tell them that I will be calling via a relay service on a specific day and time (eg. Monday between 1&2pm) then I explain that when I call they will announce they are "...relay service" and calling on behalf of myself. Typically I'll also explain that because instead of talking and listening, I type and read - that during the call someone called a "relay operator" will voice for me exactly what I type, then when "Jim" speaks the relay operator will type to me whatever "Jim" says. I also mention that the Relay Operators have to follow a special code of ethics and confidentiality so it is "safe" for them to ask for my charge card numbers, address, phone number etc during a TTY call (unlike in an email where it's not "safe" to include a credit card number etc as it can be intercepted etc).
While this may seem like a major PITA to go to all this trouble - I do find that IF I run into places that haven't dealt with Relay before, they really appreciate that I "walk them through" how to use relay, what to expect etc ... in fact I've had them thank me for explaining it to them in emails and ask for permission to send the email to all their staff to educate them on using relay etc. I tend to be one of those people who will go out of my way to help pave a path for others who are Hoh/d/Deaf - I'll spend a great deal of time explaining services, communication techniques etc to people because I know how difficult it was for me growing up WITHOUT any of that ...I use my ability to speak and sign to my advantage allowing me to explain a number of things, dispel misconceptions (espeically that people who sign "aren't smart" etc).
If I'm able to make things easier for even ONE other Hoh/d/Deaf person, I consider all the "extra trouble" time well spent.
