Magnetic save the dates and rsvp poems!
More often it's the case that your invitation has been safely stored in a drawer, perhaps with other wedding invitations (they might be very popular!) with the wedding date itself noted on a calendar BUT NOT THE RSVP deadline date.
No offence is intended, they just forgot. And when you start reminding them, they can't reply right away because they now realise they need to make sure they are free on that day and can get there, afford the expense and so on. Resulting in yet more delays to your much needed rsvp reply.
Not all guests realise how important that RSVP deadline is, thinking to themselves, if they can make it they will be there on the day. They assume if they've been invited, they will be catered for. It needs to be communicated to guests on your rsvp details, that numbers must be confirmed to the venue and caterers ahead of time. There are various way to do this which you can see via the example magnetic save the dates and rsvps featured.
Note that rsvp's don't guarantee attendance but as some guests inevitably bring uninvited +1's and children you should find it balances out.
Anecdote: I invited a work colleague and her plus1 to my wedding and she asked if her three children could also attend. I generously said yes, catered and paid for them all to attend only for my work colleague (without notice) to attend on her own. So that was 4 rsvps that did not attend, however I had some 'randoms' show up from grooms work that made up the numbers. So don't worry too much about the potential chaos of who's coming and not. Go with the flow on your big day.
HELP THEM REMEMBER
NO EXTRA COSTS
These magnetic save the dates and rsvp reminders are available in various sizes and because they're magnetic card, the cost is no more than a regular non-magnetic card invitation.
What to do if guests still don't RSVP in time
1. A week BEFORE your rsvp deadline (not on or after the deadline)
REMIND your guests the deadline is approaching. You can do this via a Facebook post, emails (guarantees they see it), texts, phonecalls.
If you wait until the deadline, they will not be able to reply immediately because chances are they haven't worked out whether they can get the time off work, arrange childcare, manage costs and so on. They will need 'more time'.
When reminding them you can let them know that due to venue size and catering, if guests haven't replied by the deadline, it will be assumed they're declining and can't attend, which is very sad as you really want them there! But needs must.
2. If NO RSVP on the deadline
You can let people know the wedding details , numbers have been finalised and how sad you are that those who didn't rsvp have opted not to attend. In other words assume they're not coming. You might get a flurry or responses and how you handle those is up to you!