We tested the hypothesis that, on the scale of a decade, earthquakes deeper than 60 km are produced at an approximately constant, that is, stationary Poissonian rate. We selected earthquakes with depths greater than 60 km to avoid the ubiquitous clusters present in shallow seismicity, without declustering the data set. Six of the 90 randomly positioned volumes contained obvious aftershock sequences and, thus, were excluded from the scoring. We showed that magnitude shifts of 0.2 to 0.4 units are present in some catalogs. Since we measure the seismicity rate above a minimum magnitude, these shifts introduce artificial fluctuations in the rate. Therefore, we modeled the influence of the magnitude shifts on the test. Measuring the goodness of fit to a stationary Poisson process model by the χ2-test for samples of 500 earthquakes each, we found that the hypothesis cannot be rejected at the 95% confidence levels based on the data in the 84 volumes without obvious aftershock sequences. We propose that this constancy of production rate is due to the effect of a constant loading rate by tectonic plate motion on an asperity assembly with a uniform distribution of current loading stress. Although this result cannot be obtained for shallow seismicity because of the presence of numerous clusters, it seems reasonable to assume that the shallow background seismicity is also produced at a stationary Poissonian rate.