RAID resyncing automatically?

This would seem to be indicating that the syncing between the 2 members of the RAID are not staying in sync with each other.

1. Investigate logs

I'd investigate your dmesg logs and see if there are any messages stating that either of the physical HDDs that make up this array are having hardware failures.

2. Check mdadm

You can also consult mdadm using the --detail switch to find out more information about the resync like so:

$ sudo mdadm --detail /dev/md0
/dev/md0:
        Version : 00.90.03
  Creation Time : Sat Jan 26 09:14:11 2008
     Raid Level : raid1
     Array Size : 976759936 (931.51 GiB 1000.20 GB)
  Used Dev Size : 976759936 (931.51 GiB 1000.20 GB)
   Raid Devices : 2
  Total Devices : 2
Preferred Minor : 0
    Persistence : Superblock is persistent

    Update Time : Fri Jan  1 01:29:16 2010
          State : clean, resyncing
 Active Devices : 2
Working Devices : 2
 Failed Devices : 0
  Spare Devices : 0

 Rebuild Status : 50% complete

           UUID : 37a3bfcb:41393031:23c133e6:3b879f08
         Events : 0.2178969

    Number   Major   Minor   RaidDevice State
       0       8        1        0      active sync   /dev/sda1
       1       8       17        1      active sync   /dev/sdb1

If both devices seem fine and you cannot pinpoint which device is having an issue, you may want to temporarily run a diagnostic tool such as HDAT2 or SpinRite against each HDD to confirm their health.

3. Cabling

If the HDDs check out then I would start scrutinizing the cabling, I typically will swap these out.

4. Controller

I'd next scrutinize the controller itself, either taking the drives out of the affected system and diagnose them in a secondary system, or add a 3rd party controller card into the affected system to diagnose the issue further.

5. Power supply

Believe it or not, I've had issues in the past with HDDs and RAIDs where swapping out a failing, or about to fail, power supply, resolved my RAID health issues.

Check your cron files, many distros do a scheduled resync/re-check once a week.

On CentOS 7.1 it's in /etc/cron.d/raid-check

# Run system wide raid-check once a week on Sunday at 1am by default
0 1 * * Sun root /usr/sbin/raid-check

To configure the behaviour edit /etc/sysconfig/raid-check

On Debian it is done from:

/etc/cron.d/mdadm

To disable:

chmod -x /usr/share/mdadm/checkarray

See also.