This is normal and is a common strategy for sellers in a multiple offer situation. Since they see they have a few interested parties, they are trying to get the potential buyers to raise their offers and get the highest possible offer. Talk to your agent about strategies for how you will proceed. Be prepared that if needed to offer you best and highest offer - make sure it's an offer that both meshes with sales comps and is a price you are comfortable paying for the home. A multiple offer situation can be tricky but try not to let it stress you out, make sure you are comfortable with your offers, and let your agent guide you through the process.
A listing agent will make recommendations, but the bank has the last word. $40,000 in 4 weeks is quite a price reduction, though. It could be that a defect or repair issue was uncovered in the property. Perhaps, a previous buyer did an inspection and found repairs were needed. Ask your realtor to speak with the listing agent. If there was a previous inspection done, the listing agent should share the negative findings with your realtor.
If you don't have a realtor, considering consulting a one for assistance. Trulia would be a great place to start.
Obtaining a pre-approval letter is the only way the seller can assure that a lender has made a commitment to give you financing. This is to avoid the property being taken off the market and then finding out the buyer's financing is not in place.
Pre-qualification letters are not worth the paper they are written on. More often than not, the loan officer has not verified the buyer's debts, assets, pay stubs, or tax returns.