I'm running Monero 'Boron Butterfly' (v0.14.0.2-release) on a Linux compaq-laptop 4.4.172 #2 SMP Wed Jan 30 17:11:07 CST 2019 x86_64 Intel(R) Core(TM)2 Duo CPU T8100 @ 2.10GHz GenuineIntel GNU/Linux

The host is behind a firewall, but that should not matter, right?

Looking at the logfile, I noticed the deamon had stopped syncing with the network.

2019-06-11 07:22:24.156 [P2P9]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [73.184.42.223:18080 OUT] Sync data returned a new top block candidate: 1853420 -> 1854404 [Your node is 984 blocks (1 days) behind] 
SYNCHRONIZATION started
2019-06-11 07:22:59.286 [P2P2]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [197.232.65.203:18080 OUT] Sync data returned a new top block candidate: 1853420 -> 1854404 [Your node is 984 blocks (1 days) behind] 
SYNCHRONIZATION started
2019-06-11 07:23:41.559 [P2P3]  WARN    cn      src/cryptonote_core/cryptonote_core.cpp:1767    There were 0 blocks in the last 90 minutes, there might be large hash rate changes, or we might be partitioned, cut off from the Monero network or under attack. Or it could be just sheer bad luck.
2019-06-11 07:24:17.347 [P2P9]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [173.255.205.142:18080 OUT] Sync data returned a new top block candidate: 1853420 -> 1854405 [Your node is 985 blocks (1 days) behind] 
SYNCHRONIZATION started
2019-06-11 07:24:46.873 [P2P3]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [149.202.94.125:18080 OUT] Sync data returned a new top block candidate: 1853420 -> 1854405 [Your node is 985 blocks (1 days) behind] 
SYNCHRONIZATION started
2019-06-11 07:25:12.708 [P2P1]  WARN    cn      src/cryptonote_core/cryptonote_core.cpp:1767    There were 0 blocks in the last 90 minutes, there might be large hash rate changes, or we might be partitioned, cut off from the Monero network or under attack. Or it could be just sheer bad luck.

Issuing an status command:

2019-06-11 09:18:57.934 [P2P2]  WARN    cn      src/cryptonote_core/cryptonote_core.cpp:1767    There were 0 blocks in the last 90 minutes, there might be large hash rate changes, or we might be partitioned, cut off from the Monero network or under attack. Or it could be just sheer bad luck.
status
Height: 1853420/1853420 (100.0%) on mainnet, not mining, net hash 279.46 MH/s, v11, up to date, 8(out)+0(in) connections, uptime 2d 5h 39m 48s

I'm told that I'm 100% in sync, but the blockheight is wrong.

After restarting the daemon, normal sync is resumed.

2019-06-11 09:23:27.579 [P2P3]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:1598
**********************************************************************
You are now synchronized with the network. You may now start monero-wallet-cli.

Use the "help" command to see the list of available commands.
**********************************************************************
2019-06-11 09:23:29.052 [P2P1]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [13.231.81.228:18080 OUT] Sync data returned a new top block candidate: 1853420 -> 1854469 [Your node is 1049 blocks (1 days) behind] 
SYNCHRONIZATION started

And a little later:

2019-06-11 09:45:46.807 [P2P9]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [95.216.159.70:18080 OUT] Sync data returned a new top block candidate: 1853880 -> 1854483 [Your node is 603 blocks (0 days) behind] 
SYNCHRONIZATION started
2019-06-11 09:46:21.479 [P2P8]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:1182        [13.231.81.228:18080 OUT]  Synced 1853900/1854483
2019-06-11 09:47:44.852 [P2P8]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:1182        [13.231.81.228:18080 OUT]  Synced 1853920/1854484
2019-06-11 09:48:39.150 [P2P8]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:1182        [13.231.81.228:18080 OUT]  Synced 1853940/1854483
2019-06-11 09:49:36.577 [P2P2]  INFO    global  src/cryptonote_protocol/cryptonote_protocol_handler.inl:310 [107.191.99.95:18080 OUT] Sync data returned a new top block candidate: 1853940 -> 1854484 [Your node is 544 blocks (0 days) behind] 
SYNCHRONIZATION started

Would you mind compiling master to see whether that fixes the issue?

https://github.com/monero-project/monero#compiling-monero-from-source

The host is behind a firewall, but that should not matter, right?

Whilst it results in you not being able to serve the blockchain to others, it does not inhibit the daemon (monerod) from syncing properly.