Você pode ver o último tempo de montagem com tune2fs (para sistemas de arquivos ext *). Exemplo no Debian 7:
root@wheezy:~# tune2fs -l /dev/sda1
tune2fs 1.42.5 (29-Jul-2012)
Filesystem volume name: <none>
Last mounted on: /
Filesystem UUID: 4b7e1b6a-a6ff-47a8-be65-d4c32c05dcf5
Filesystem magic number: 0xEF53
Filesystem revision #: 1 (dynamic)
Filesystem features: has_journal ext_attr resize_inode dir_index filetype needs_recovery extent flex_bg sparse_super large_file huge_file uninit_bg dir_nlink extra_isize
Filesystem flags: signed_directory_hash
Default mount options: user_xattr acl
Filesystem state: clean
Errors behavior: Continue
Filesystem OS type: Linux
Inode count: 1893120
Block count: 7572480
Reserved block count: 378624
Free blocks: 7127797
Free inodes: 1843283
First block: 0
Block size: 4096
Fragment size: 4096
Reserved GDT blocks: 1022
Blocks per group: 32768
Fragments per group: 32768
Inodes per group: 8160
Inode blocks per group: 510
Flex block group size: 16
Filesystem created: Wed Oct 12 10:04:11 2016
Last mount time: Mon Jan 30 09:53:03 2017
Last write time: Mon Jan 30 09:53:03 2017
Mount count: 5
Maximum mount count: -1
Last checked: Wed Oct 12 10:04:11 2016
Check interval: 0 (<none>)
Lifetime writes: 3503 MB
Reserved blocks uid: 0 (user root)
Reserved blocks gid: 0 (group root)
First inode: 11
Inode size: 256
Required extra isize: 28
Desired extra isize: 28
Journal inode: 8
Default directory hash: half_md4
Directory Hash Seed: 01c6a9d1-d5fe-41d7-9fa7-8a5a96c5dbed
Journal backup: inode blocks
Para nfs você pode ver o parâmetro age em /proc/self/mountstats - em segundos.