Can private keys be exported more than once in Electrum client so long as the've not been spent?
It seems like you don't understand how Bitcoins, private keys and bitcoin addresses work, so I'll make it simple:

As I explained to you here https://bitcoin.stackexchange.com/a/11479/2467 , you should not (more like MUST NOT) export your private keys from an Electrum seed. This can compromise all your private keys.

Your private keys are derived from your seed every time you make a payment to sign the transaction. So there's no need to see them, the client calculate them for you, use them, and hide them again. all you need is to keep your seed safe.

If you want to know the balance in your offline Electrum wallet's addresses you can use a seedless wallet on an online computer. To do that look for your Master Public Key in the offline Electrum, and restore from your MPK on an online computer.

You don't need your private keys to know the balance on their public addresses anyway. Public addresses are public and if you have already received on them, you can check their balance on Blockchain.info