Answering service on landline says it is full after on message

I bought these phones for my grandma who is hard of hearing hoping they would work for her and her hearing aids. We continually are having problems with the answering service inbox being full after one message and friends and family cannot leave messages. I know I can clear the voicemail, but it shouldn’t have to be done every time. Is there a way to remove it entirely? It’s like the voicemail is overtaking the answering service and my 92 year old grandma doesn’t want to have to delete them every single time one message comes in. Thank you.