@BellesAndGraces I would, I take money in advance for a course of dog training lessons or behaviour modification sessions.
If someone doesn't cough up on time, I might well give their slot to someone else, I am in demand, I do not need to piss about chasing people.
The reminder to pay up is the invoice. As we will have communicated via email and probably telephone, and I'll have told them I am sending an invoice, it is up to them if they want my services, to follow up if they then do not receive it. Not my job to double check they got it.
When I did home visits I also took money in advance for new clients, and on the day for existing ones (these were one off 'as and when' rather than part of a regularly scheduled package deal). If I had a cancellation less than 24 hours prior I would require half the visit cost. If I turned up and they were not there, they'd have to pay the full cost for the consultation and pay for the rescheduled consultation at the time of booking... and on the rare occasion it happened, they did.
It may seem harsh or unusual to you but being self employed it is necessary, paying others is never anyone elses first priority. Their priority, as evidenced in this thread, is themselves.
It's all information clients have presented to them before they sign up, if they don't like it they absolutely can go elsewhere.
Hopefully OP has learned some lessons here, particularly about priorities and what terms and conditions on invoices actually mean.