BEA has repeatedly declined Oracle's offer, claiming that it will sell up to any company willing to pay $8.3bn. Oracle's offer represented $17 per share, but BEA is asking for $21.
Oracle said that it will not put in a new offer, but did urge BEA's shareholders to pressure the board.
"We asked the BEA board to allow their shareholders to vote on our $17 per share proposal. They chose not to," Oracle said in a statement.
"If the BEA shareholders are unhappy with the behaviour of the BEA board it is up to those shareholders, not Oracle, to take the appropriate action.
"The BEA shareholders should not assume that Oracle will renew its $17 per share offer in the future.
"Over time many things can change: BEA's business might materially weaken, the stock market can fall further from its recent record highs, or Oracle may have committed its capital elsewhere."
More recently BEA has been pushing into the market for service oriented architectures, but has yet to establish itself as a leader.
The company has been the subject of acquisition rumours for some time. The situation is creating uncertainty with prospective buyers about whether they can stake their future on the software.
BEA's revenues also highlight a decline in new software sales, indicating that the vendor is failing to attract new customers.
Analysts do not consider an acquisition a matter of 'if', but of 'when'.
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