There are things you can do when you submit your offer to encourage the seller to accept your contract. One thing is to include an escalatory clause that states how much you are offering but that you will offer $500 above any higher competing offer up to a certain amount. It needs to also include that the seller must show you evidence of the higher offer before your contract is changed to reflect the higher price. This is especially useful in a multiple offer situation. However, some sellers agents do not notify us that the property has multiple offers before they accept one.
If your offer is rejected and another offer accepted, you can also offer a "back-up" contract. That way, if the first contract does not close, you are next in line to get the home, without competing with multiple offers again. The "back-up" contract must be negotiated just like the original offer and fully executed. Therefore, you will need to offer the seller something that you did not offer the first time, like higher price or better terms.