PNG files contain more image data than JPEG files. Depending on the size of the PNG file, this may exceed the MMS maximum size limit which is between 600 kb and 3.5 MB per photo. This might explain the error message. Reducing the size of the PNG file or converting it to a JPEG file may help.

Thanks for your reply. 

The PNG in the most recent example is only 75 kB. 

Which phone do you have?

Have you tried restarting your phone?

If no luck there, try resetting your phone’s network settings. This may resolve glitches the network may be having. This does not erase any user data, but you will have to re-enter Wi-Fi passwords and re-pair Bluetooth devices (if applicable).

Some large PNGs are transmitted, some are not. Some recipients have problems, some do not. This inconsistency suggests a network problem rather than a device problem. 

Which messaging app are you using?

Ask the recipient(s) which messaging app they are using. This might solve the problem of file sending/receiving inconsistencies.