I saw that there is a firmware update available for my R11e-LTE-US modem. However, when I try to update the firmware on the modem, the cellular connection drops and it will not reconnect until I disable and re-enable the modem. The firmware update instructions say that updating over-the-air is the only way to update the firmware on this modem. How can I keep the connection from dropping while downloading the update? Or, is there another way to download and install the update? I am running RouterOS 7.1.5.

When you run the command on terminal:
The modem will download the firmware and upon installing the lte will drop and that is normal... You should not do anything until the terminal informs you that the installation is done...
If for some reason it won't install it will indicate that it has failed...
After that the modem will automatically initialize again and get to Running status...

So, if you followed the above steps and you get a fail, let us know...

Also check here https://help.mikrotik.com/docs/display/ ... areupgrade

I tried it again and ran: /interface/lte/firmware-upgrade lte1 upgrade=yes
I waited about 10 minutes and got status: failed.

As soon as it started downloading, the LTE interface unregistered. I looked at the Traffic tab and saw that there was no TX/RX traffic at all. It looks like the upgrade is failing because the LTE connection drops. It loses the connection to the Internet, so it cannot download the update, and it eventually fails. After failing, the LTE interface regained connectivity and it is still on the old firmware version.

Upon firmware upgrade procedure the LTE will show as not Running... If i remember right that is at the installing phase...
That is normal...

I would suggest you reset the device to defaults, uninstall any extra packages ( if added ) and retry to update the modem...

I am following post Unable to update firmware on R11e-LTE-US modem, but none of the suggestions are working not via the LTE modem itself or eth1 with internet conncetion.
Somewhere it did say Mikrotik can provide a file R11e-LTE-FW-Upgrade.zip which will work via an usb to PCIe interface but you will need to contact Mikrotik support to obtain this.
How can I obtain R11e-LTE-FW-Upgrade.zip from Mikrotik ?

I guess you could contact the support https://mikrotik.com/support