Weeks, even months of mixed signals from Vice President Joe Biden about his presidential intentions are increasingly testing the patience of Democrats who have otherwise been sympathetic to his family concerns, and the window of opportunity for him to emerge as a desired alternative to Hillary Rodham Clinton’s candidacy appears to be shrinking.

Since resuming work in late summer after the death in May of his eldest son, Beau, the vice president has alternately stoked speculation that he might join the Democratic field and said he lacked what he called the emotional fuel to do so.

But factors beyond his control are intruding on Biden’s deliberations. Outside ruminations on his tragic personal history have had the inadvertent effect of giving his grief an off-putting veneer of opportunism. On Thursday, a person close to the vice president said Biden was hoping that a group backing him would not air a widely publicized ad that refers to his family tragedy.

The group, Draft Biden, subsequently announced it would not air the ad.