update: a number of data points have rolled in and I feel pretty comfortable stating that this is a generally applicable rule. How close the applications need to be is up in the air, but 30 days seems to be the maximum limit.
Recently, Bank of America has approved some different-day credit card applications, using an applicant’s existing credit file (without issuing an additional hard pull). Bank of America is known to combine hard pulls for same-day applications, but not different-day applications.
Data points are scant at the moment, but my assumption is that this can only happen when the applications are within 30 days and for personal cards.
If you have any recent data points for BOA (different-day applications in 2016, within 90 days of each other), please share them in the comments or use this handy Google form, which tracks a wide scope of information. American Express have also been doing something somewhat similar as well (approvals without a hard pull). It’s possible this means that the lack of a hard pull is due to the way that the consumer reporting agencies, rather than the card issuers themselves. If you have noticed this recently with any other card issuers, please let us know in the comments.