The critical issue is meeting your offer's obligations timely: removing any contingencies, getting your loan funded, etc.
Seldom would you have to use the lender who gave you pre-approval. Generally to meet your specified times you won't have time to "shop" for a lender. Your real estate agent may recommend a lender who may be better for a number of different reasons: quicker funding, have already approved the HOA, etc
Unfortunately, pre-approval doesn't guarantee the loan will be funded quickly. Your lender should be giving both you and your real estate agent honest information about what can be done and how to avoid issues.
Basic real estate mortgage information at http://julianalee.com/reinfo/mortgage.htm
Top 2 agent nationwide at Keller Williams Realty, the nations largest
Over 20 years experience
Over 1,000 homes sold in Santa Clara and San Mateo Counties