Additives can lose their solubility and transition to a suspended state in a lubricant for a variety of reasons. Heavier additives, such as solid extreme-pressure additives, foam inhibitors and some anti-wear additives, can simply separate due to extended storage times. While it is uncommon for antioxidants to separate quickly due to storage conditions, it is worth noting that the less controlled the environment in which the oil is stored, the quicker the additives will separate. Engine oils have the shortest shelf life due to the heavy additive load they carry and thus should be used as quickly as possible to mitigate any problems associated with separation.
Contamination can also cause additive precipitation. Most additives in lubricants are polar by nature, which means they have an affinity for other polar objects. Contaminants such as dirt, moisture and wear metal are polar as well, so they attract additives. As additives build up on contaminants, they begin to settle out or are separated by filters. This removes the additive from the oil and impacts the health of the lubricant.
Some additives are filtered out due to their size. This is a problem that occurs mostly with anti-foam agents, as they are larger and often suspended rather than dissolved in oil. If the filter's pore size is too restrictive, it can lead to additive buildup on the filter's surface, thus removing additives from the bulk of the oil.
In addition, as the oil flow changes pressure and temperature, it can affect the solubility of the additives and some contaminants. In this case, as oil flows through the venturi, it experiences a drop in pressure. This rapid change in pressure may be enough to cause some of the dissolved additives to come out of solution and precipitate on the machine surface and in the filter. This can be observed in some varnish-removal methods in which oil is stressed in a similar fashion to force varnish precursors to come out of solution, allowing them to be filtered and removed. This scenario could be a likely culprit in the situation described above, but there may be other factors as well.
For instance, the engine in question is a gasoline engine. Depending on the gas that fuels the engine, contaminants could be impacting the oil's surface tension and its solubility for additives. The more contaminants such as water or the more degraded the oil due to hydrocarbon contamination, the more prone the oil would be to dropping additives and allowing them to come out of solution in a venturi or filter. It would be a good idea to find out if anyone else is running the engine on a similar gas and having the same issues. Switching to a different base oil could reduce the problem and may also result in longer drain intervals.
While it's difficult to pinpoint the exact conditions that are causing the crystallization of the BHT, the leading culprits are likely a contaminant from the fuel and the base oil's intolerance to it.