This is definitely the most common error message you will get if you have trouble sending e-mails using your server and unfortunately, this error message does not tell you how you can solve the issue.
Technically, the phpMailer library (a famous php library to send e-mails... used by AcyMailing and Joomla) tried to send a message using the php mail() function and the php mail() function returned "false".
This kind of web server does not have a mail server so you can't send e-mails from your local server.
What's the solution? Well, you should configure AcyMailing to use an external SMTP server instead of using the php Mail function to test Acy but you can consider it will work on your live server
Your mail server may refuse to deliver your message if the receiver e-mail address is not a valid one... So if you have this "could not instantiate mail function" for only a few of your subscribers, it may just be because their e-mail address is not valid!
Some mail servers will refuse to deliver your message if it contains special characters in the subject such as a quote or a comma or any other kind of special character (ùïä)...
Please create a new Newsletter, specify a standard subject line ("test" for example) and give it a new try.
The same way, some mail server will refuse to deliver your message if the sender information contain special characters.
Please go on the AcyMailing configuration page, turn OFF the option "add Names" and give it a new try.
Add Names option turned OFF
Some mail server may not authorize you to deliver your message if the subject line is too long...
Change your subject line to a single word to make sure it's not a problem of subjet length.
Some servers won't accept to deliver your message if you specify a bounce e-mail address. Others will force you to apply a bounce address which belongs to your own domain...
Please go on the AcyMailing configuration page and leave the bounce address field empty.
Just like the previous point, some servers will only deliver messages if you specified a bounce e-mail address belonging to your own domain.
If removing the bounce e-mail address didn't work, you should try to add it again and make sure it's a valid e-mail address belonging to your own domain.
Most of hosting company will allow you send X e-mails per hour. If you go over that limitation, the mail server will refuse to deliver more e-mails and will display this error message. So for example if you successfully sent 480 e-mails and you can't send e-mails any more, then it's probably what happened and you should first wait one hour to deliver more e-mails and also make sure AcyMailing is configured to stay below your sending limitations.
Some hosts won't enable you to send multiple parts... That definitely a parameter we recommend you to keep enabled but you should try to turn it OFF to see if that solves the "could not instantiate mail function" issue. You will find this option under the "Mail Configuration" tab on the AcyMailing configuration page.
Some hosts will not allow you to send a message with an attachment... so if you have this issue only on Newsletter with attachments, you could turn OFF the option "embed attachments" on the Acy configuration page to make sure Acy will add the file as a link in your message and not as a real attachment.