Repeatedly sending coins from an address to itself Let's say I create an address that has a balance of x bitcoins, where x is the minimum transaction amount before prompting a fee. Hypothetically this address is used as a permanent cryptographically secure mechanism that sends itself x coins at certain points which have some significance. 

Will miners mine this transaction over and over or will it eventually be ignored by the network?

Will this transaction be readable by parsing the blockchain, or is it handled differently? 

Will this transaction ever eventually incur fees and thus never be put into a block (since the wallet will never own more than x BTC)?
Nodes don't check the history of a coin or address to determine whether to include or propagate it, so it will be possible to send coins from an address to itself multiple times.

However, the priority of a transaction depends on how aged its inputs are. If you try to do it too frequently, you'll be using young inputs, lowering the priority and making a fee necessary.