The importance of the deposit to the transaction

The agreement of purchase and sale clearly states that the deposit is payable "upon acceptance" of the offer. That means what it says, and not two or three days later. If you know the deposit is going to be late, or there is some sort of challenge in this regard, then a clause should be added to the offer specifying when the deposit will be received.
If the deposit is not received, the deal is technically "dead", meaning that the buyer may be free to buy another property or the seller may be free to sell to another buyer. It all gets very gray, should the problem go to court and a decision is made based on the individual circumstances. It is certainly a situation in which nobody wants to find themselves involved.
When an agent works for the seller, we must be insistent on receiving the cheque immediately. The selling agent should have the cheque when they drop off the accepted offer. If the offer is done by fax, then the selling agent should be insistent on the getting the cheque right away. If the cheque is slow in coming, it is incumbent on the agent to inform their seller that the cheque has not been received, and the implications that could this could create.
When an agent works for the buyer, it make perfect sense to get in the habit of getting the cheque right away, when the offer is being done. Don't wait until everything is done and act like it is an afterthought.