Partitions mounted with 'errors=remount-ro' option will be remounted as read-only automatically, if a kernel detects an error.
I suggest you to dig a little deeper, because there is a possibility a hardware problem is the source of inconsistency error.
You need to provide us with more information about your OS setup and hardware.
Output from these commands should be a good start:
$ cat /etc/fstab
$ sudo blkid
$ sudo smartctl -iHA /dev/sda
$ sudo smartctl -iHA /dev/sdb
"smartctl" is a tool from "smartmontools" package.
The output will be long, so you can post it at "https://paste.debian.net/"; with reasonable expiration date and send us just a link to it.