Instagram has a switch that decides whether connected tools like Ellipsend can handle your DMs. It's usually on already. When it's off, Instagram messages don't arrive in Ellipsend and messages to Instagram contacts don't send.
Check it when Instagram DMs aren't arriving or sending and the first checks in Messages Aren't Arriving: The Connection Checklist didn't fix it.
Turn It On in the Instagram App
You need a phone that's logged in to the Instagram account you connected to Ellipsend.
Open the Instagram app and go to your settings.
Tap Messages and story replies.
Tap Message controls.
Under Connected tools, turn on Allow access to messages.
You can also get there from your DMs. Tap the three dots, then Tools, then Message Controls.
Check the Setting on Your Facebook Page Too
Your Facebook Page has a matching setting. On facebook.com, switch into the Page your Instagram account is connected to. Then open Connected Instagram and make sure Allow access to Instagram messages in Inbox is on.
The link only works once you've switched into the Page. How to Give Ellipsend Control of Your Conversations shows how to switch.
After You Turn It On
The change takes effect right away. To test it, send your Instagram account a DM from another account. When it shows up in the inbox, reply to it.
Messages that came in while the switch was off may not appear in Ellipsend.
Still Not Arriving
Go back to Messages Aren't Arriving: The Connection Checklist and work through the remaining checks. If you've used another DM tool on this account, How to Give Ellipsend Control of Your Conversations is the next place to look.