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Do pending transactions live forever on Eligius mempool?

Nothing is forever imho. Just until restart.
Anyway, only Luke-Jr can answer this question.

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I've been watching this 16-of-16 multisig tx for a while (2ee6d8ea223e118075882edba876f01b30f407eb6c6d31c40bd6664a17f20f0c)... it has never been redeemed even though the solution is not hard to arrive at.

My conclusion is that someone has been spamming Eligius with a valid redemption tx but it is never included in a block due to insufficient fees. But because it is already in the mempool, no other valid tx can be accepted.

So does that mean the tx can never be redeemed?

How did you try to redeem this output? There is a web-form http://eligius.st/~wizkid057/newstats/pushtxn.php but we do not know is it connected directly to the pool-node-accepting-non-standard-txs or not. The second way is connect to the node with non-standard client and send raw tx from console. But what is Eligius ip-address?

I was interested also in this question. So, I wrote a program which parses the whole blockchain, locates all spendable-by-me outputs, connects to Eligius (nat.router.dashjr.org:8333 but I am not sure), asks for memory pool (this is important), resolves conflicts (pool will not accept my double-spending attempt) and sends redeem transaction.

I sent the redeem transaction with the fee 0.00010000 from several inputs (including my standard inputs from my account and this one) today. Next time I run my program the transaction came to me from the pool - so I definetetely know that it was correct and was accepted. Wow! But it was not mined for several hours - may be the fee is too low or this node is not a pool, but only a Luke's node with old client on it.

tx hash is bb1ebbe8855043440037260250c5c048a400106c535d7ef0b4dd95069c4316cc
(it was not accepted by all other standard nodes, so you can not google it until (and if) it will be mined)

Code:

"txid" : "2ee6d8ea223e118075882edba876f01b30f407eb6c6d31c40bd6664a17f20f0c",
"vout" : 0,
"scriptSig" : {
"asm" : "0 30450221009dda0de70d944bac4d077088e5dd80ded212bfc9f79f36e2636387800ed81bfe022016a18a1c4352975e6497834bdd5ead22f3d031e62bf66e6fc2174184bb0367f701 OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP OP_DUP",
"hex" : "004830450221009dda0de70d944bac4d077088e5dd80ded212bfc9f79f36e2636387800ed81bfe022016a18a1c4352975e6497834bdd5ead22f3d031e62bf66e6fc2174184bb0367f701767676767676767676767676767676"
},
"sequence" : 4294967295

I can discard this transaction (by double-spending my standard outputs on the rest of network) and resend to Eligius with higher fees. Let's wait a couple of days.

By the way. This node (nat.router.dashjr.org) holds thousands of spam transactions 1Sochi&1Enjoy in it's memory pool. Is it a bug or a feature? I dont know. But if it is Eligius - so it keeps pending transactions for a looooong time - month or two or may be more.

Sorry for my poor English