We present the results of an expanded, long-term radial velocity search (25 yrs) for evidence of binarity in a sample of seven bright proto-planetary nebulae (PPNe). The goal is to investigate the widely-held view that the bipolar or point-symmetric shapes of planetary nebulae (PNe) and PPNe are due to binary interactions. Observations from three observatories were combined from 2007-2015 to search for variations on the order of a few years and then combined with earlier observations from 1991-1995 to search for variations on the order of decades. All seven show velocity variations due to periodic pulsation in the range of 35-135 days. However, in only one PPN, IRAS 22272+5435, did we find even marginal evidence found for multi-year variations that might be due to a binary companion. This object shows marginally-significant evidence of a two-year period of low semi-amplitude which could be due to a low-mass companion, and it also displays some evidence of a much longer period of >30 years. The absence of evidence in the other six objects for long-period radial velocity variations due to a binary companion sets significant constraints on the properties of any undetected binary companions: they must be of low mass, <0.2 M(sun), or long period, >30 years. Thus the present observations do not provide direct support for the binary hypothesis to explain the shapes of PNe and PPNe and severely constrains the properties of any such undetected companions.
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