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You search AAA-BBB-CCC and see R0 but later just search BBB-CCC and see R>0?

Or you search AAA-DDD-BBB-CCC and R>0 but not the same number as BBB-CCC shows?

Why does AAA-BBB-CCC shows R=0 but the other routes R>0 (but not always the same amount)???

This is related to how fare class availability to created for multi-segment trips.
The fare class availability is displayed as the minimum of each same fare class inventory of all the segments. So if looking for a T fare, all the segments need to have T fare inventory. If any one is T=0, then the multi-segment results is 0 or whatever the minimum inventory is.

This is true for R --- but the good news is upgrades will clear based on individual segments (except in the case of Direct flights).

So in the above case, regardless of routing the BBB-CCC segment can clear on application of certs or miles.

The general recommendation is to search for the critical upgradeable segments individually -- note the R availability. Then book the desired multi-segment trip and apply the upgrade.
In the slim chance the R space disappears in the meantime, you can make use of the 24 hour free cancellation window to start-over.