Thank you for your query.
To begin with, I am assuming you are using Full control modem mode, so the fact that LEDs are blinking and you are unable to see modem information via WEBUI is completely normal. Full control modem disables any statistics are provides full control of the modem to the end device.(Your pc) In other words, it disables gsmd service running on a router. However, if you are using partial control modem mode, then such behavior is not normal. In addition, the fact that you are loosing mobile connectivity is strange as well, mobile connectivity should recover and you should be able to access the internet regardless of the modem mode you are using.
Unfortunately, I was not able to replicate the issue at my end, therefore, I would like to clarify a bit regarding the issue you are having:
1) Are you using Full control or partial control modem mode?
2) Can you still access the device after reconnecting power? (Test this please, setup your modem to work via RS-232 and disconnect the power supply, then connect the power back and check if you are able to access the device via SSH/WEBUI, also check whenever you have mobile connectivity and also check when ever you still can control the modem via RS-232. For example, type in the command: AT + COPS? to show information about your mobile internet provider)
In addition, Could you please go to System -> Administration -> Troubleshoot and download the troubleshoot file. Forward this file to me via private message please.
Note: If you are using full control mode, test this with partial control mode and if the mobile connectivity does not come back up, please follow the steps mentioned earlier to obtain the troubleshoot file. Since the troubleshoot file will indicate modem information only in partial control mode, I would prefer if you could try replicating this problem on partial control mode and forward it to me.