Huh. Have you actually been able to complete the old ones? Because I tried that once early on, and it didn't seem like the counters were moving on one from the previous day. However, I don't remember what it was exactly, so I can't be sure I wasn't making a dumb mistake or misreading something.

I completed four different gifts last night (one from yesterday, and three from last week). I hadn't done anything for any of them yet other than picking them up from the pile by Ikora.

If the counters weren't moving, it's likely that you were needing "blue" planetary resources instead of their "green" counterparts -- and in fact I've heard reports that the wording used in the UI is not always consistent/accurate. If you need 10 of something - you need the green ones, if it's asking for 3 - you need the blues (which you can "advance" by taking one blue and putting it in the vault and taking it back out repeatedly).

That's totally not true. If you pick up a gift, it will stay in your inventory and you can pick up the next day's gift, even if you haven't completed the previous one.

I'm not sure why I thought you couldn't do that (other than an expectation from three years worth of unfriendly design I guess).

Maybe I'm just an idiot, but there's your PSA for the day.