There is a link between significant change and deterioration in dementia, with moving being high on the list of causes. It is therefore avoided unless necessary. Usually that would be when the person's needs increase to a point where they cannot be met safely in the current environment, e.g. residential level to nursing (where there is a qualified nurse on the unit 24/7) or 'elderly frail ' to a dementia unit with more staff and security.
As others have said, due to the volume of laundry done in care homes, clothes do get 'redirected' with other residents' belongings. It can help to put a room number on as well as the name. If other things are going missing, staff can look at other measures to address that. It's often another resident who no longer grasps the concept of personal belongings or space.
Dealing with multiple, changing managers is frustrating and difficult for staff too. My suggestion would be to
a) collate notes from previous meetings. If you don't have any, they should be on the home's files. Ask them to collate and ask for copies if you don't have them already.
b) arrange a meeting with the current manager and their manager. This may be the owner if it's a small enterprise but larger organisations will have a higher management structure. They should provide a suitable person.
c) compile a document that lists the issues you have raised and what agreements were reached, when and by whom. If you now feel that you would like to discuss other options, state that too.
d) ask that the meeting is minuted and request a copy.
e) state that unless issues are addressed and mitigated as much as possible, you will be looking for alternative support for the gentleman.
I have to wonder, though, how they are justifying such a huge cost increase, especially as the gentleman has such low needs. It might also be worth speaking to Social Services about their agreed rates and what they would pay when the savings threshold is met. If they would not pay the current home's fee levels, he would perhaps need to move at that point. They may also be able to give you some local options that you can research. Check the CQC (in England) report online and ask around. You would learn a lot by visiting the top choices and speaking to the managers there. Watch how staff are interacting with residents. Ask about staff ratios. Speak to residents or their family about their experience. The homes that look nice don't necessarily provide the best care. Good management, staff and general cleanliness are more important.
Finally, expensive does not necessarily equate to good. As LPA you also have a duty to make good financial decisions for your relative.
It's a really tough decision to make but if you do the groundwork you will at least have all the relevant information to work with. Good luck! 🙂