The Social Security Administration (SSA) does not decline people a certain amount of times when they apply for benefits. There is no policy or procedural reason for this.
Most often, people keep applying repeatedly when they’re turned down for benefits. These applications will be turned down each time. If you’ve been denied benefits, the proper procedure is to file an appeal, not to reapply for the same case.
Having legal representation can increase your chances of winning your appeal. Contrary to popular belief, however, there is no set amount of applications or appeals after which the SSA takes applications more seriously or after which they’re more likely to approve benefits. If you get turned down, you need to file an appeal.