Read your contract's clauses for the following:
1. SERVICE levels. If you have agreed service levels and the vendor is in breach of those, you have recourse under the escalation process.
2. ESCALATION process. If your contract defines an escalation process, you may want to first escalate the service level breaches following the process outlined there to get remedies.
3. SERVICE credits. If your contract specifies service credits (i.e., amounts you can deduct from the invoice for breaches of SLAs a.k.a. penalties), invoke them. Nothing gets attention like dollars and cents. Ensure that you have this right specified in the contract.
4. TERMINATION clause. If you have a "Termination with cause" clause, you may want to use that to cut your losses and is invoked after the escalation process fails. Typically, these have an "opportunity for cure" language to provide the vendor an opportunity to cure the issue. If there is a "Termination for convenience" clause, that is a leverage you have as a last resort. (Typically, you just have to give X days notice that you are terminating it and fulfill the obligations under that clause).
Talk to your vendor relationship manager (i.e., the vendor's official representative, if mentioned in the contract) and document the issues in writing. Agree on any remediation steps in writing with dates/timelines and joint reviews.
Internally, talk to your legal team to understand your options under the contract and also your rights and obligations. (Don't underestimate the legal team's values in this exercise. They can very quickly tell you what to do.)
Good luck.
Having payment start from day one is a basic mistake that companies make, usually you can pay for consulting up until the point of go live, then turn on the recurring payment. Making sure bug severity vs resolution time is in writing is another key item to add.
Unless you spelled out the SLA and requirements in a contract, you are looking at an ugly court case where you need to claim they are in violation of the 'spirit of the contract'. If they have written down that their service is poor, and you have these examples in writing, it might be possible.
As far as rebates go, why would you want to continue a detrimental relationship with a vendor? Usually you would want to exit and find another solution.
Stories like these fascinate me. On one hand, you have companies like these that get away with such poor service while our own B2B SMB SAAS company goes above and beyond for customers for almost a tenth of the cost and we still sometimes get the short end of the stick. Guess we should charge more :)
Unfortunately, I am currently in the first part of a yearly contract fully pre-paid. This is because I didn't really anticipate that a real, legitimate company that maintains significant infrastructure might simply shrug and say, well, our shit doesn't work so suck on it. I filed for cancellation and requested a rebate after trying to get them to fix things for several months but they flatly denied it and claimed that in fact, their TV service is "free" and not actually included in the (internet) contract at all. They've also written the TV T&Cs in such a way that they literally say the entire service might not work at all for indefinite periods or forever, and you have no recourse.
This strikes me as complete horsecrap and after checking my local laws, I'm pretty sure they're in violation of several aspects of warranty and agreement law. Next step is to get legal advice. The laws in question boil down to:
1. You may not disclaim all liability/warrantee rights, regardless of what you put in your contract.
2. Consumer agreements that are totally one sided aren't valid.
I don't know if there are any equivalents for B2B contracts, but this sort of rule is pretty common around the world. You can't actually be completely negligent when selling things, even if you get people to theoretically sign away their rights.
After encountering this nightmarish customer support I googled around a bit and wasn't hugely surprised to discover their staff flaming customers on Twitter and claiming they (the customer) were guilty of "hate speech". Not really amazed to find a correlation between those sorts of beliefs and crap, unprofessional service. Wish I'd known about it before.