The slowness is because Elasticsearch, in version 1.3.7, had to compare every local segment with every segment already in the snapshot repository. This caused snapshot speed to become increasingly slower as more snapshots (and therefore more segments) were added to the cluster.
This was addressed in a later version of Elasticsearch (I can't find the exact pull request, or even version number, but I believe it was resolved in the 2.x releases). The solution is to upgrade. 1.3.7 is no longer supported, nor are any of the 1.x branches. The 2.x branches will cease to be supported when Elasticsearch 6.0 is released (later this year).
If that does not work for you, potential workarounds include:
- delete older snapshots, reducing the segment count in the repository.
- change to snapshot to a new repository every week, or month. This means every time you snapshot to a new repository, it will be a full snapshot, increasing storage requirements.