Who rejected your offer, the owner or the bank?
Let's assume the owner rejected, perhaps with the guidance of a trusted advisor.
It is very relevant to understand if the listed $70,000 was reflective of current condition. Area comparable sales for authentic properties may have recently sold for $140,000. This would suggest the listed price was reflective of the condition of the house.
Now you must consider if the $70,000 is the teaser price, obviously way below market value. The intent is to stimulate multiple offers from which the owner can choose or subsequently suggest highest and best offer. This is very important when considering the possibility of a bank counter.
Finally, your offer to purchase at $45,000 is only part of the story. Were there ANY contingencies, financing or other issues that could compromise the process. At $45,000 you need a 'slam-dunk' absolute cash offer, as is, where is, close tomorrow. Slamming the door to tight on a low-ball offer will not inspire further conversation with seller. Your trusted advisor can create for you the framework for a proper strategic position.
Then of course, as mentioned earlier, the bank has the final say. Should the bank counter your $45,000 with $60,000, $70,000 and yes it is possible the bank could counter at $100,000 if BPO supports value, and if you are unwilling to come up with the balance, everyone involved has wasted their time.
Yes, everyone is looking for a bargain, but the 'too good to be true' ones don't exist. Really good values are available for those who are decisive, competitive, know the facts and able to respond quickly.
How do I judge your offer? Sorry, don't have all the facts.