  Very long baseline interferometry (VLBI) provides the highest-resolution
images in astronomy. The sharpest resolution is nominally achieved at the
highest frequencies, but as the observing frequency increases so too does the
atmospheric contribution to the system noise, degrading the sensitivity of the
array and hampering detection. In this paper, we explore the limits of
high-frequency VLBI observations using ngehtsim, a new tool for generating
realistic synthetic data. ngehtsim uses detailed historical atmospheric models
to simulate observing conditions, and it employs heuristic visibility detection
criteria that emulate single- and multi-frequency VLBI calibration strategies.
We demonstrate the fidelity of ngehtsim's predictions using a comparison with
existing 230 GHz data taken by the Event Horizon Telescope (EHT), and we
simulate the expected performance of EHT observations at 345 GHz. Though the
EHT achieves a nearly 100% detection rate at 230 GHz, our simulations indicate
that it should expect substantially poorer performance at 345 GHz; in
particular, observations of M87 at 345 GHz are predicted to achieve detection
rates of $\lesssim$20% that may preclude imaging. Increasing the array
sensitivity through wider bandwidths and/or longer integration times -- as
enabled through, e.g., the simultaneous multi-frequency upgrades envisioned for
the next-generation EHT -- can improve the 345 GHz prospects and yield
detection levels that are comparable to those at 230 GHz. M87 and Sgr A*
observations carried out in the atmospheric window around 460 GHz could expect
to regularly achieve multiple detections on long baselines, but analogous
observations at 690 and 875 GHz consistently obtain almost no detections at
all.
