The ring current, an equatorial near-Earth current, fluctuates in response to solar wind plasma interactions with Earth's magnetosphere. Despite extensive research on storm-time ring current energization, direct evidence of the energy transport into the inner-magnetosphere that powers this current remains scarce. Recent observations revealing that very-near-Earth reconnection (VNERX, occurring at geocentric distance <14 R-E) can occur during storms suggest that such reconnection could play an important role in ring current development. Here we address how common VNERX is. We use inner-magnetosphere and plasma sheet observations from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellites spanning 13 years. During this period, THEMIS observed 512 storms and 7 VNERX events. All VNERX events occurred during storm main-phase at or near the pre-midnight sector (None were observed during storm recovery-phase.). The events occurred within 1 R-E of the modeled neutral sheet, suggesting that VNERX events are elusive because they lie near the neutral sheet. Since THEMIS spent 5,253 hr within 1 R-E of the modeled neutral sheet during storm main-phase, the inferred observational VNERX occurrence rate is 1.3 per 1,000 hr of storm main-phase. This rate is lower than published ion-diffusion-region occurrence rates seen in the near-Earth plasma sheet during non-storm times (likely substorms). These results suggest that while VNERX events might be significant for the storm-time ring current's initial buildup (during storm main-phase), other transport mechanisms, like enhanced global convection, may be responsible for maintaining the strength of the ring current during storm recovery-phase.