16:18:31 INFO]: [Statz] Statz v1.3 has been enabled!
[16:18:31 INFO]: [Autorank] Enabling Autorank v3.8.4
[16:18:31 INFO]: [Autorank] Simple config file loaded
[16:18:31 INFO]: [Autorank] Advanced config file loaded
[16:18:31 INFO]: [Autorank] Settings config file loaded
[16:18:31 INFO]: [Autorank] Internal properties file loaded
[16:18:31 INFO]: [Autorank] Backup data file loaded (backup-data.yml)
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_a ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_b ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_c ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_d ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_e ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_f ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_g ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_h ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_i ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_j ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_k ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_l ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_m ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_n ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_o ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_p ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_q ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_r ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_s ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_t ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_u ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_v ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_w ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_x ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_y ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_z ...
[16:18:31 INFO]: [Autorank DEBUG] Loading uuids_other ...
[16:18:31 INFO]: [Autorank DEBUG] Loaded stored uuids.
[16:18:31 INFO]: [Autorank] Loaded playerdata.
[16:18:31 INFO]: [Autorank] Found Statz plugin: Statz (by Staartvin)
[16:18:31 INFO]: [Autorank] Hooked into Statz (by Staartvin)
[16:18:31 INFO]: [Autorank] Loaded libraries and dependencies
[16:18:31 INFO]: [Autorank] Interval check every 5 minutes.
[16:18:31 INFO]: [Autorank] Total data file loaded
[16:18:31 INFO]: [Autorank] Daily data file loaded
[16:18:31 INFO]: [Autorank] Weekly data file loaded
[16:18:31 INFO]: [Autorank] Monthly data file loaded
[16:18:31 INFO]: [Autorank] Language file loaded (lang.yml)
[16:18:31 INFO]: [Autorank] Using timings of: autorank
[16:18:31 INFO]: [Autorank] Autorank 3.8.4 has been enabled!
[16:18:31 INFO]: [Autorank DEBUG] Autorank debug is turned on!
[16:18:31 INFO]: Server permissions file permissions.yml is empty, ignoring it
[16:18:31 INFO]: CONSOLE: Reload complete.
[16:18:31 INFO]: [Autorank DEBUG] Updating leaderboard 'TOTAL_TIME'!
[16:18:31 INFO]: [Autorank DEBUG] Size leaderboard: 0
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_players'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_joins'
[16:18:31 INFO]: [Vault] Checking for Updates ...
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_deaths'
[16:18:31 INFO]: [Autorank DEBUG] Updating leaderboard 'DAILY_TIME'!
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_items_caught'
[16:18:31 INFO]: [Autorank DEBUG] Size leaderboard: 0
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_blocks_placed'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_blocks_broken'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_kills_mobs'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_kills_players'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_time_played'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_food_eaten'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_damage_taken'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_times_shorn'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_distance_travelled'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_items_crafted'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_xp_gained'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_votes'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_arrows_shot'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_entered_beds'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_commands_performed'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_times_kicked'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_tools_broken'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_eggs_thrown'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_worlds_changed'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_buckets_filled'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_buckets_emptied'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_items_dropped'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_items_picked_up'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_teleports'
[16:18:31 INFO]: [Statz debug] Loaded table 'statz_villager_trades'
[16:18:31 INFO]: [Autorank DEBUG] Updating leaderboard 'WEEKLY_TIME'!
[16:18:31 INFO]: [Autorank DEBUG] Size leaderboard: 0
[16:18:31 INFO]: [Statz debug] Statz is connected to its database!
[16:18:31 INFO]: [Autorank DEBUG] Updating leaderboard 'MONTHLY_TIME'!
[16:18:31 INFO]: [Autorank DEBUG] Size leaderboard: 0
[16:18:31 INFO]: [Vault] No new version available
[16:18:34 INFO]: [Autorank DEBUG] Saving all data files...
[16:18:34 INFO]: [Statz debug] Save Statz database.
[16:18:35 ERROR]: [Autorank] Disabling Autorank: Vault was not found
[16:18:35 INFO]: [Autorank] Disabling Autorank v3.8.4
[16:18:35 INFO]: [Autorank DEBUG] Awaiting termination of MySQL thread...
[16:18:35 INFO]: [Autorank] Autorank 3.8.4 has been disabled!
[16:18:44 INFO]: [Statz debug] Save Statz database.

Nope:
[12:20:32 INFO]: [Statz debug] Vault has been found but cannot be used!

So, apparently it's Vault fault.. but why only some users have this problem?
Beside this, Vault seems working normally..

It means that economy plugin or permissions plugin is not properly found by Vault. Could you provide your whole log of startup?

Does Statz find Vault?