If rejected, you can continue to make higher offers.

I had a couple of deals get rejected as they just did want to move enough off there list price. 

I just had this come up, read "Rejecting the pain in the butt applicant without getting sued" in Bigger Pockets, those people wanted to pay a year upfront as well.

Joel, I had that deal evaluated by a local lender a little over 15 months ago that could lock in 3.59 for 15 years (this is precisely why I have heartburn over losing it), but I did not heavily shop it because I found a great newer multifamily below replacement cost shortly after being rejected by the bank on the retail strip.

I had one approved by the seller then 3 months later rejected by the bank.

Hello,       Have a property to rent out and in about 3 weeks, I have received about 20 enquiries and I have rejected all of them till now, mainly because of their income to rent ratio of 3:1 hasnt worked out or the credit score is not right ( even after benefit of doubt) etc. 

I'll still present the offer to my seller, but with huge caveats and a recommendation to reject the offer.

Possibly, if you have rejected other applicants and closed down your advertising efforts.

We had no idea every Title company in town would reject us and not have a clue how to fix the situation.

The more rejections I get the better it will get.