First of all, the question seems to misunderstand what "union elections" are about. They do not involve forming or joining a union. Under 29 USC 157 all employees have the right to form or join any union at any time. No election is needed. 29 USC 159 provides that:
Employees shall have the right to self-organization, to form, join, or assist labor organizations, to bargain collectively through representatives of their own choosing, and to engage in other concerted activities for the purpose of collective bargaining or other mutual aid or protection, and shall also have the right to refrain from any or all of such activities
The above section is part of the National Labor Relations Act (NLRA) of 1935, as amended and updated. It is found in [Chapter 7 of 29 USC] (https://www.law.cornell.edu/uscode/text/29/chapter-7)
A union is formed as the voluntary act of its members. A union generally has a constitution that controls its operations. This will specify under what conditions the union will be dissolved. An individual may leave a union at any time.
Elections, such as those mentioned in the question, are held by the National Labor Relations Board (NLRB) when employees desire that a union become the designated collective bargaining representative for a bargaining unit (which is a group of employees deemed to have a "community of interest"). There is considerable flexibility in just which employees shall be designated as a bargaining unit. In the event of a dispute, this is resolved by the NLRB. (see 29 USC 159(b)). Elections may also be held when there is a desire by some workers to change representatives.
A petition requesting a representation election can be filed by a union, a worker, or an employer.
Under 29 USC 159(a) the representatives for a bargaining unit: "shall be the exclusive representatives of all the employees in such unit for the purposes of collective bargaining in respect to rates of pay, wages, hours of employment, or other conditions of employment". That is what representation elections are about.
A union, or other organization, is supposed to be recognized or designated as the bargaining representative for a bargaining unit (BU) only if a majority of the workers in that BU who make a choice want that representative.
In addition to being certified by the NLRB after winning an election, a union can be recognized as the representative voluntarily by the employer on the request of a majority of the employees. Or such a request can trigger a secret ballot election.
My question is, how often can unionization votes be held?
Representation elections are normally held no more often than once a year in any BU. Specifically, 29 USC 159(c)(3) provides that:
No election shall be directed in any bargaining unit or any subdivision within which in the preceding twelve-month period, a valid election shall have been held.
Cases recently in the news where a second election has been ordered or proposed in a shorter period of time involve cases where it has been held, or alleged, that the previous election was not valid because of unfair labor practices.
An election can also be held to decertify the bargaining representative, or to substitute a new representative. In all these cases a majority of the workers voting must agree for any change to be made. The "no more than once per year" rule applies to all these elections.
If there are more than two choices on the ballot (for example, if several different unions are proposed, perhaps along with "no union") and no one choice gets a majority, a runoff is held between the two choices with the largest number of votes. This is specified in 29 USC 159(c)(3)
All representation elections are held under the authority of, and are regulated by, the NLRB.
So when a union is formed, a company is no longer allowed to hire any worker outside of the union?
This is not correct. That is what is known as the "closed shop", and it is illegal under the NLRA. Arrangements that are legal (when they are part of a collective bargaining agreement (CBA)) under the NLRA are:
The "union shop". On being hired, an employee must join the union within a specified time (which must be at least 30 days, but may be longer). This is specifically permitted by 29 USC 158(a)(3). However, many states have by state law prohibited union shop agreements.
An "agency shop". No employee need join any union, but any employee must pay the designated bargaining representative a fee (normally less than the union membership dues) for its efforts in representing the workers of that BU, and that worker specifically. Some states have by state law prohibited or limited agency shop agreements.
An "open shop". No worker need pay any dues or fee to any union or other representative., But if the representative is a union, its policies are set by the union members, and to become and remain a union member, a worker must pay union dues.
Aside from any shop agreement included in a CBA, 29 USC 158(a)(3) provides that it is an unfair labor practice (ULP) for an employer:
by discrimination in regard to hire or tenure of employment or any term or condition of employment to encourage or discourage membership in any labor organization ...
It is also a ULP (under 29 USC 158(a)(2)) for an employer to:
dominate or interfere with the formation or administration of any labor organization or contribute financial or other support to it ...
The provisions of the NLRA and some proposals that have been made to change it are summarized and explained in "The National Labor Relations Act (NLRA): Union Representation Procedures and Dispute Resolution" from the Congressional Research Service (CRS). This report goes into more sub-topics than this answer calls for. As far as I can tell, it correctly describes the current law. See https://www.everycrsreport.com/about.html for more info.