HM Revenue and Customs (HMRC) has extended a July 31 deadline to August 6 for the 550,000 people at risk of losing their payments.
The Revenue body said it had taken the decision because people faced "long delays" trying to get through to its renewal phoneline due to industrial action taking place this week. The phones traditionally get busier as the cut-off for renewals looms.
The Public and Commercial Services Union (PCS) is staging rolling action in various parts of the UK on Wednesday, Thursday and Friday to highlight its concerns about staff shortages.
For the first time, HMRC is offering people renewing their claims this year the option of doing so online, at gov.uk/renewtaxcredits. Claimants can also renew by calling 0345 300 3900.