Learn English – had proposed or proposed

This is a tricky question. The native ear will immediately recognize that "had been remained" is not correct. The had should be followed by a past participle. Remained and been are both past participles; you can use one or the other, but not both.

So, either of these could be used to start the sentence:

• He had been president for 20 years...
• He had remained president for 20 years...

This issue gets tricky, however, when you switch to the passive voice. In that case, you can use he had been followed by a past participle, as in:

• He had been elected 20 years ago...

That's a valid formation, and it's listed as the past perfect passive verb form in this table¹:

So, the question becomes, why can the verb elected be used in this way, but not the verb remained?

The key is that the sentence with elected is using the passive construction, but the sentence with remained has an active construction. As Dave Sperling says on his ESL website:

Because subjects of passive verbs receive the action, verbs that cannot have objects (intransitive verbs) do not have passive forms.

If you look up the words in a dictionary, you'll see that elect is transitive, and remain is intransitive, which is why had been remained sounds so awkward to the native ear, while had been elected sounds just fine – although many native speakers might have a hard time explaining why.

Now, you can explain it for them: "It's because remained is an intransitive verb, so it cannot be used in the passive voice."

As you say, what you would ordinarily say is

This is the watch that I lost.

If you are required by the imbecility of testwriters to use a perfect, it must be a past perfect.

Because you now have the watch, you cannot say that you have lost it (except in a very unlikely 'experiential' sense of the perfect). Consequently, only the past perfect would be at all likely.

• CORRECTION, thanks to Sydney: It is also possible that you don't have the watch but are "showing a photo of" it; in this case the present perfect would be appropriate—but not required.

However, the past perfect is not required; in fact, it is inappropriate unless there is in the discourse some salient past time to which the perfect is related. For instance:

Officer Thomas arrested me for behaving suspiciously, even though I told him I was looking for my watch. But my friend Joe went back and found it, right where I was looking. This is the very watch that I had lost!