Is it possible for a fund raising deal with a venture capitalist to fall apart after a term sheet has been executed?
If so, what are some common reasons why deals fall apart at this stage?
That depends on what you mean by "term sheet has been executed".
If you mean that a startup has been given a term sheet by a VC - then yes, everything can still fall apart quite easily - for one, due diligence hasn't yet been completed. More specifically, term sheets are usually non-binding, often have conditional clauses, and of course, the VC is usually the party with the most leverage/power.
Rand Fishkin of (seo)Moz wrote an excellent post about his adventures in exactly this scenario: http://moz.com/rand/misadventures-venture-capital-funding/