The customer experiences that the connection has been failed by unknown factor.
Your right, the original sounds unnatural. I see three problems, and you've correctly identified two of them. I'll address them each individually.
The customer experiences that the connection has been failed by unknown factor.
I don't think experiences is a very fitting verb in this context. On a personal level, systems failures are something you observe, not experience. That said, this is a tricky one, because it is okay for a company to issue a statement saying:
We have experienced too many system failures over the past month.
because the speaker is talking from a corporate perspective, not a personal one. From a customer perspective, though, I'd say that customers can experience heartache, frustration, or disappointment, but not system failures, or lost connections. Instead, I would choose a verb such as notices or observes.
The customer experiences that the connection has been failed by unknown factor.
This is the wrong verb tense. When a system crashes, and we use the verb fail, we say that it has failed, not that it has been failed. Once again, though, this is tricky, because we can say:
The system has been down for over two hours!
The customer experiences that the connection has been failed by unknown factor.
I don't think by is the right preposition here. I think you are trying to say because of (or due to). If you want to stick with a preposition, use for instead of by.
Also, I think you need to put the word some in front of unknown factor, or else make it plural. When words such as reason or factor are in a prepositional phrase, we generally use some (or an indefinite article) when using the singular. For example, I might say either of these:
For some unknown reason, the connection was lost.
For unknown reasons, the connection was lost.
But I would not say:
For unknown reason, the connection was lost.
Put all of these changes together, and we get:
The customer experiences notices that the connection has been failed by because of some unknown factor.
Or, without the crossed-out words:
The customer notices the connection has failed because of some unknown factor.
As mentioned previously, the phase due to could be used in place of because of.
By the way, I agree with oerkelens; at the end of the sentence, I think reason or cause would be a better word than factor. My final edit would be:
The customer notices the connection has failed due to unknown causes.