Hey elle - the problem with the second link is basically that there’s no twitter:card markup in the page itself, so there’s nothing for our card crawler to build a card from. I don’t think this is related to your recent switch to https.
To prove this, I did the following (it may look a bit technical, but it shows the problem)
$ curl -A Twitterbot https://gingerbread.org.uk/content/2314/We-are-the-1-in-4 > out.html
$ grep twitter: out.html
<meta name="twitter:card" content="summary_large_image">
<meta name="twitter:site" content="@gingerbread">
<meta name="twitter:title" content="Families come in all shapes and sizes">
<meta name="twitter:description" content="We’re calling on companies to recognise the 1 in 4 families headed by a single parent so they receive a fair and just deal.">
<meta name="twitter:image" content="https://gingerbread.org.uk/uploads/media/1/9861.jpg">
$
Looks good, but…
$ curl -A Twitterbot https://gingerbread.org.uk/content/2322/Maintenance-matters > out.html
$ grep twitter: out.html
$
No content in the second case.
