It must be your network/firewall problem that's causing this issue and even though you cannot access Electrum for whatever reason, your funds are not lost, no matter how small/big of the amount they were, just export your private keys by going to Wallet> Private Keys> Export and you will get the private keys of all the addresses and you can import the private key of the address which contains the funds to whichever wallet you're using.
That actually turned out to be untrue for me. I'm having the same problem with the wallet stuck synchronizing and I exported the private key and when I try to sweep it with armory I'm told " The private key you have entered is actually not valid for the elliptic curve used by bitcoin (secp256k1). Almost any 64-character hex is a valid private key except for those greater than fffffffffffffffffhoishadoiashdashoi, Please try a different private key.
Afaik, that's not the problem of Electrum but Armory which doesn't supports compressed keys CMIIW. You would get better help if you ask this in Armory subsection as I have never ever used Armory wallet and don't know how it works.
A dirty workaround is, make a blockchain.info wallet, import the private key there and send all the funds from that address to your Armory wallet address. Although, I am sure there is a better solution which Armory guys might have, so ask there first and leave this option as the last resort.