Your situation is quite same with me.
After prepare all the docs, my SA submitted the loan to 3 banks which is Public bank, Maybank & RHB bank to compare all the interest rate. (Heard from my SA said RHB offer the lowest rate)
He submitted it on Monday. Tuesday morning I got a call from public bank to confirm about the loan, no interview needed. In the afternoon, I received from Maybank regarding about the loan, had a interview with the officer about 10-15 mins.
Wednesday, RHB called me in the afternoon, interviewed for around 10mins, was told by the officer that the rate is 2.5%
Friday morning got a SMS from maybank regarding the loan had been approved and the interest rate is 2.64 % . I was told by SA that my Public bank had been approved too, rate is 2.72 %.
RHB told my SA that other supporting docs is needed for the loan in the evening. Im thinking WTF, you need those supporting docs you should tell earlier in the morning, so I can prepare it and submit on that day and proceed it earlier. I do not have any transport already as I have trade in my car earlier, I need a transport badly. But due the interest rate they offer, sabar abit.
Friday evening after working hour, delay again 2 days due weekend.
Next Monday evening, check the status, pending.... Tuesday afternoon, check again, still pending........... Directly tell my SA to cancel RHB, straight away take Maybank and call them to prepare the agreement, to be surprise that he told me that I can sign the agreement on Wednesday (Within 24hrs) if I'm willing to sign it at their branch.
Gao dim everything in the Wednesday, agreement signed, paid the balance and insurance everything and pass all the docs to my SA.
I'm thinking that my car should be delivery around 2 weeks, but my SA told me that the due date for delivering my car is 15 working days. 15 days is not long, but if you realize that 15 working days are not included public holiday, weekend this and that it actually take around 3 weeks ++ !!
I told my SA that I need a transport badly and call him to delivery ASAP if possible, and he said he will try his best. I had get a confirmation date to collect my car last week, it's 3 weeks exactly , 21 days after I Gao Dim all the things. But my SA apologize to me also la, he said that his company arranged it, he can't do anything and complain also, coz the delivery date not overdue also..
What to do is only wait only now

I think my case is different from yours. This is the first time I am buying a car with my own name as my current car was a 15 years old Honda that I got it from my parents which is creaking with lots of failing components. So I wont blame the bank to be suspicious with my bank account considering my rather different situation as I work from home under a small company. I got offered with 2.54% from RHB while I got quoted 2.7 from Public Bank and 2.6 from Hong Leong.
Just had a call with RHB a couple of minutes ago, they wanted even more information. I guess its gonna drag on quite long I guess.
If its Australia, things might be easier since I have a good credit standing with the banks there and XV cost less there too. However, in Malaysia, I dont which is tough to get loan approvals. My number plate is still on the waiting list too. I think i'll only get my car in June.
I still can use my old creaking car so I guess my situation is alright.