Unless there is some sort of written agreement between you and the other shareholders which controls when the business may be shut down, the business is controlled by the Florida Business Corporations
Act, Fla. Stat. § 607.0101 (2012) et seq.
Thus, only a majority vote is required to dissolve a company:
§ 607.1402. Dissolution by board of directors
and shareholders; dissolution by written consent of shareholders
(1) A corporation's board of directors may propose dissolution for submission to the shareholders.
(2) For a proposal to dissolve to be adopted:
(a) The board of directors must recommend dissolution to the shareholders, unless the board of directors determines that because of conflict of interest or other special circumstances it should make no recommendation and communicates the basis for its determination to the shareholders; and
(b) The shareholders entitled to vote must approve the proposal to dissolve as provided in subsection (5).
(3) The board of directors may condition its submission of the proposal for dissolution on any basis.
(4) The corporation shall notify each shareholder of record, whether or not entitled to vote, of the proposed shareholders' meeting in accordance with s. 607.0705. The notice must also state that the purpose, or one of the purposes, of the meeting is to consider dissolving the corporation.
(5) Unless the articles of incorporation or the board of directors (acting pursuant to subsection (3)) require a greater vote or a vote by voting groups, the proposal to dissolve to be adopted must be approved by a majority of all the votes entitled to be cast on that proposal.
(6) Alternatively, without action of the board of directors, action to dissolve a corporation may be taken by the written consent of the shareholders pursuant to s. 607.0704.
So, unless the Articles of Incorporation require that your shares also are needed to approve the dissolution of a company, the company can be dissolved by a majority vote. Assuming that the other 60% shareholders approved, this would be legal and would not be something you could sue for.
Please let me know if you have further questions.