Since you asked about any jurisdiction, and presumably any common law jurisdiction, in which one of the elements of theft is the intention to permanently deprive the owner of the property, here's the UK* answer.
Regarding borrowing specifically, the UK statute referring to theft - the Theft Act 1968 - provides for this in section 6(1):
A person appropriating property belonging to another without meaning the other permanently to lose the thing itself is nevertheless to be regarded as having the intention of permanently depriving the other of it if his intention is to treat the thing as his own to dispose of regardless of the other’s rights; and a borrowing or lending of it may amount to so treating it if, but only if, the borrowing or lending is for a period and in circumstances making it equivalent to an outright taking or disposal.
In other words, a thief may say 'I only wished to borrow it', but that won't necessarily amount to a defence under English law. It depends on how long (s)he borrows it for, and how (s)he treats it while borrowing it.
In addition, the case law clarifies what is meant by 'his intention is to treat the thing as his own to dispose of regardless of the other's rights'. This has been held to mean:
- Selling, Bargaining with. R v Cahill, R v Lloyd
- Rendering Useless. DPP v J
- Dealing with in a manner which risks its loss. R v Fernandes, R v Marshall
- Borrowing in certain circumstances. R v Lloyd
- Pawning. s6(2) Theft Act 1968
- Not enough to just deal with it. R v Mitchell
So how do we prove whether someone intended to deprive the owner of the property permanently, or at least permanently enough to amount to an offence under the Act? The answer seems to be that we look at how they deal with it, and what condition they leave the property in. If they do any of the things listed above, with the exception of no. 6, then they have demonstrated an intent to permanently deprive; if they merely use the property, then that isn't enough to show such intent.
You asked specifically:
I am looking for an answer that explains whether someone who credibly asserts – e.g., by advance sworn affidavit – that they intend to return the item can be convicted of theft, or any other crime, for taking someone else's property for an extended but not infinite period of time.
In the case of R v Lloyd, the court held borrowing would become intention to permanently deprive the owner of the property if 'all goodness, virtue and practical value is gone'. So if someone swore they were planning on returning the item, the court could nonetheless convict them of theft if they held on to the item for so long, and treated it as their own to such an extent, that all its value was gone. (In R v Lloyd, the items in question were films, and as they were returned in much the same condition as they'd originally been in, this was held not to be intention to permanently deprive, and therefore not to be theft.)
*By 'UK' I mean 'English and Welsh'; the answer may be different in Scotland.