Hey pbertling,
We'd be happy to help you find a solution. We understand your mother-in-law is experiencing drops in cellular service while using the Visible eSIM in her iPhone 11.
Given that the phone itself has been replaced, it's unlikely to be an issue with the iPhone's hardware, and you did a great job isolating things further by moving to eSIM too. At this point, we'd suggest working through the following steps for issues with No Service or Searching for cellular data:
Restart your iPhone or iPad
Restart your device. If you're not sure how to do this, follow these steps to restart your iPhone or restart your iPad.
Check for a Carrier Settings update
To manually check for and install a carrier settings update:
1. Make sure that your device is connected to a Wi-Fi or cellular network.
2. Tap Settings > General > About. If an update is available, you'll see an option to update your carrier settings.
3. To see the version of carrier settings on your device, tap Settings > General > About and look next to Carrier.
If you insert a new SIM card into your iPhone or iPad, you need to download the carrier settings for your new carrier.
Take out the SIM card
After removing the SIM card, put it back in.
• If the SIM card is damaged, or doesn't fit in the SIM tray, ask your carrier for a new SIM card.
• If you transferred your SIM card from another device, ask your carrier if your SIM card works with your iPhone or iPad.
Learn more about removing your iPhone SIM card or iPad SIM card.
Reset your Network Settings
Go to Settings > General > Transfer or Reset [Device] > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before.
Update your iPhone or iPad
Update your iPhone or iPad to the latest version of iOS or iPadOS.
Contact your carrier
Issues with your carrier or account might affect your service. Contact your carrier to:
• Verify that your account is active and in good standing.
• Make sure that there are no outages in your area.
• Check that your device isn't blocked from receiving cellular services and is set up with the right data plan.
All this information and more is available here: If you see No Service or Searching on your iPhone or iPad - Apple Support
As it mentions above, if the issue persists after completing these steps, please reach out to your wireless carrier Visible for further assistance from here.
Take care!