Sorry. 
Elsewhere in the world (I’m thinking of Canada), you might have a real problem as an employer if you misword the termination clause in a contract, even unintentionally, because it might invalidate more than just the clearly illegal part. (That wouldn’t necessarily stop a large company from doing it anyway – intentionally or not.)
In Taiwan though, an illegal termination clause is a problem in the sense that the illegal part can’t be enforced, but I haven’t seen a case in which it caused any trouble for the employer beyond that. I would love to be corrected about this if I’m missing something.
Anyway, the first thing that must be established if you want to have your contract recognized as permanent is that you are a permanent resident. You have an open work permit, so I’ll assume that’s because you’re a PR.
Just in case, I’ll also mention that if you are merely a foreign spouse, you do not have a permanent (non-fixed term) contract, unless they changed that rule while I wasn’t paying attention.
I’ll also assume your job is subject to the Labor Standards Act, as most jobs are. (Ask the labor department if you have any doubt about this.)
The definitions of those terms are found in the LSA Enforcement Rules, Art. 6. A one year contract is not temporary, short-term, or seasonal. However, a specific work (特定性工作) contract can be for up to one year, or longer with the approval of the labor department. So most likely, your contract is a specific work contract for a fixed term.
Sorry, but why do people let employers get away with that?
Assuming your contract is for specific work, the second contract rule doesn’t apply because of LSA Art. 9 Par. 3:
前項規定於特定性或季節性之定期工作不適用之。
The preceding paragraph shall not apply in the case of a fixed term contract for specific or seasonal work.
(This kills the entire Par. 2, not just Par. 2 Subpar. 2, so even if your employer allowed you to continue working after the expiration of the first contract before giving you a second contract, it still doesn’t count.)
You would still have a contract, just not a perfect one. Afaik that would not be a sufficient reason to invoke LSA Art. 14. As I said though, the current contract is probably a fixed term contract.
If the contract is supposedly for a fixed term but actually for continuous work (i.e. the form of the contract doesn’t match the substance), the clause setting the duration of the contract is invalid, and the contract is deemed a non-fixed term contract. This assumes, of course, that nothing but the wording of that one part of the contract stands in the way of it being a non-fixed term contract. I wouldn’t rely on the fact (hypothetically) that the employer wants the worker to continue working for as many years as possible, because the employer’s decision to use specific work contracts gives the employer an easy way out of that.
One thing to understand about lawsuits in Taiwan is that in most cases you can’t win big damages. If the employer spent a lot of money recruiting you or training you or risks missing out on a huge amount of business because of your early departure, then it makes sense to sue you. Otherwise, the amount of money to be gained is probably not much more than the lawyer’s fee, if even that, so the employer would likely view it as a waste of time. (The losing party pays the court fee but not the winning party’s lawyer’s fee.) Of course, the option still exists.
As always, I suggest talking to the labor department and/or a lawyer.