I think it’s largely down to how your employer decided to run the scheme rather than a legal rule by HMRC or any of the cycle scheme providers.
Local council I worked for stipulated 12 months employment before it was allowed, current employer it’s out of probation period (which can be anything between 3 and 12 months depending on the job role).
A colleague at my current company was told he could not have a new voucher for two years after his first voucher had expired. He challenged this as there was no stipulation of it in any of the providers rules nor the company’s HR or payroll rules.
After some to-ing and fro-ing, the company decided to allow new vouchers when one and run out and indeed, Cyclescheme invite you to request a new voucher when they email you to advise you of the “final deposit’ payment.