Conwy County Borough Council has admitted facing "significant pressures" in its nappy collection service.
The council said it could "only provide limited assurance" on collections, citing staff shortages and vehicle issues.
This comes after concerns were raised about missed collections, with nappy and incontinence product collections meant to be weekly.
In response to a letter from Janet Finch-Saunders MS, the council said: "Staffing these rounds is becoming more and more challenging.
"Following recruitment and training and learning the collection rounds, staff quickly move on so we are in an ongoing cycle of trying to establish consistent collections which inevitably means the service is not in the position we want it to be in."
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Ms Finch-Saunders highlighted the impact of this on residents, saying: "I know of situations where there are a few weeks’ worth of nappies in containers awaiting collections.
"For example, one resident has mentioned a build-up of 21 nappies in the bin.
"Others are reporting to me that there is a stench coming from the containers, which is made worse by the missed collections and prolonged collection times.
"Whilst I appreciate the explanation provided by the Local Authority, serious questions need to be answered as to why there are staffing problems, and alternative solutions put in place.
“Leaving nappies for weeks on end is not acceptable nor hygienic."
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