We report on calcium abundance A(Ca) estimates during the decay phases of 194 solar X-ray flares using archived data from the Bent Crystal Spectrometer (BCS) on the Solar Maximum Mission (operational 1980-1989). The abundances are derived from the ratio of the total calcium X-ray line emission in BCS channel 1 to that in neighboring continuum, with temperature from a satellite-to-resonance line ratio. Generally, the calcium abundance is found to be about 3 times the photospheric abundance, as previously found, indicating a "first ionization potential" (FIP) effect for calcium, which has a relatively low FIP value. The precision of the abundance estimates (referred to hydrogen on a logarithmic scale with A(H) = 12), is typically ~± 0.01, enabling any time variations of A(Ca) during the flare decay to be examined. For a total of 270 short time segments with A(Ca) determined to better than 2.3% accuracy, many (106; 39%) showed variations in A(Ca) at the 3σ level. For the majority, in 74 (70%) of these 106 segments A(Ca) decreased with time, and for 32 (30%) A(Ca) increased with time. For 79 out of 270 (29%) we observed constant or nearly constant A(Ca), and the remaining 85 (31%) with irregular time behavior. A common feature was the presence of discontinuities in the time behavior of A(Ca). Relating these results to the ponderomotive force theory of Laming, we attribute the nature of varying A(Ca) to the emergence of loop structures in addition to the initial main loop, each with its characteristic calcium abundance.