In the Wikidata UI when creating two new statements A and B which share the same property and publishing for example statement A then the other statement B is displayed as if it had been saved too. Hence, there's no longer a "Publish"-button on statement B. However, once reloading, only statement A is displayed and statement B is lost. When looking at the entity's version history only the publishing of statement A has been recorded.
Additionally, in Firefox' network inspector I observed that only one POST-action=wbsetclaim-request is made, namely for statement A so I would suspect that this is an UI-specific issue.

Reproduce

Please refer to the attached video for a demonstration of this issue. That video has been recorded on test.wikidata.org using the Timeless-theme, however, I initially explored this issue on wikidata.org using Vector. For reproducing this issue I blanked my global.js, therefore I would claim that gadgets and user-JavaScript is not relevant.

1. Open an entity data item.
2. Click on "add statement". Let's say we are creating statement A.
3. Enter a property, let's say P1.
4. Enter some value.
5. Click on "add statement".
6. Enter the same property as for statement A. Let's say P1.
7. Enter some value.
8. Click on "Publish" for statement A.

Thoughts

I'm having some suspicions on the presence condition for this issue. I suspect that…

1. this issue only occurs when there has been no previously created statement with the same shared property.
2. both statements A and B must be in different statement group views (which, if the first suspicion is fulfilled, is always the case since the UI provides no option to add a value to a group view with the right property)