to miss an appointment/date

e.g.

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to let the appointment/deadline lapse

I'd say; it can be as "ambiguous" as the German.

Yes, I would use "pass", not "lapse." "Lapse" would refer more to some kind of license, insurance, visa, certification, etc. that one doesn't renew, so I can't agree with dude on this one.

In the case of a deadline, I would use "to let (the deadline) pass" if it's on purpose, or, as Sch.Lawiner suggested above, "to miss (the deadline)" if it's accidental.

For an appointment, I would use "to miss" if it was an accident, or "to skip" if it was on purpose. I don't think we have an ambiguous word that fits correctly.

 

Maybe:

I let the appointment slide.

Letzteres ist wohl das gebräuchlichste im Business Jargon, wenn man irgendwas bis zu einem Zeitpunkt nicht liefert (abhängig vom Kontext).

z.B. Termin ohne Reaktion verstreichen lassen (weil man nicht wie vereinbart antwortet) --> miss the response deadline

I don't quite understand your sentiment there. One can most certainly renew a license, visa, or insurance (policy), for instance. But more to the point: deadlines can also lapse, as can appointments, although those admittedly could be of a slightly different sort. But here are some lapsed deadlines:

lapse of the deadline

Most of the limited partners have indicated a willingness to let the deadline lapse, these people said.

The New York Times

Televisa let the deadline lapse, the executives said, in part because an investment partner, the Carlyle Group of Washington, dropped out of the consortium ...

If it's literally coming down to the deposit deadline, can we just let the deadline lapse and assume they know we are not attending? 

In recent years, Congress has regularly let the deadline lapse but has eventually come up with the money in time to let sales- resume.

etc., etc.