Inviting yourself or attempting to be invited to a party is one of the biggest social taboos. It will be seen as disrespectful by the host. One problem with it is that if you ask if you are invited to a party, and the host didn't intend to invite you, they are put in the socially difficult situation of having to say "no" to you in person, or to bow to pressure and say "yes" to avoid this awkward situation, but which can lead to them resenting this later.
This is the case even with the biggest parties: weddings, milestone (21/30/40/50) birthdays, funerals. If you don't want to risk being seen as disrespectful or being resented, don't ask someone if you're invited to a party.
There are some fairly straightforward reasons you may not have got an invitation.
- They don't enjoy having you at parties with them for whatever reason.
- They don't want too large a party and have limited it to closer friends or family.
- They intended to invite you but you haven't got the invitation yet.
So while there could be a rejection of you personally, there's a good chance the reason is relatively innocent and not personally a rejection of you.
There is not much you can do, unfortunately, to enquire about which it is now. The issue with asking "are you planning anything?" is that at this stage, the question can readily be identified as disingenuous: they will already know there's a good chance you've seen it on Facebook already and that therefore the question is not genuine. And, it's at the point in time when the party would have to be planned already if there was one. This question is only without risk if you ask it before they are likely to have planned the party or invited anybody.
Invitations are often lost in the mail (weddings typically send invitations in snail mail) and people often miss out of going as a result. You can only really mitigate this as host: confirm by text message or email in addition to sending the formal invitation. One time, we realised after the fact that a few guests did not attended parties for our kids because their invitations were lost; we'll try to confirm by email or text when we can.