To clarify your question, both ISO/IEC 17025 and ISO/IEC 17020 are conformity assessment standards, so an organization would be accredited, not certified against them – ISO 17025 for a laboratory, and ISO 17020 for an organization performing inspections.
what do they need to do in order to maintain their certification?
As with all accreditations against international standards, the organization would need to maintain their own management system internally, continuously meet all the requirements, support their own quality objectives, manage risks and address opportunities for improvement. There are various monitoring and evaluation of trends that is required. For example, a laboratory must monitor its performance by comparing it’s results with other laboratories. To maintain accreditation status, organizations would be audited by their Accreditation Body at intervals (according to the accreditation cycle), to assess and peer review the extent to which they are maintaining the system.
Is there a requirement to update to the latest iteration?
Yes indeed. A transition period is provided, usually three years after the revision publish date. During this time an organization must address, meet the new requirements and be assessed by the Accreditation Body.
If so, how often do they need to do so?"
All ISO standards are reviewed every five years and revised if considered necessary. If they are revised, organizations are required to transition to the new revision.