HI
The Transition Properties box remains greyed out if "No Transition" is selected in the transition window but the default transition duration is shown. (This value may or may not be the duration seen under ToolsOptions/Editing...See below)
Clicking the X between clips and then selecting a transition will open a window allowing a selection between keeping clip positions fixed or moving the clips, (in effect overlapping them) (Version 4.58)
Once you have selected a transition and it is in place, re-clicking the X in order to possibly change the transition, will once more bring up the list window where now, the Transition Properties button **will now be active** and will allow you to alter the duration of the transition. This duration will remain in force for that particular transition. Adding a transition to a different point in the project will once again grey out the properties box until a transition is selected and also the default duration will have reverted to the value set under Tools/options/Editing, not the value set in the previous clip
If you already have a transition in place and you try to change the duration in the properties box to a value that is too long for the clips you won't be able to do so but entering the same value (depending on the choice made between moving the clips or leaving them fixed etc) may truncate the clips or extend the transition to cover both clips, even if they have been truncated. (Complicated ;-) )
As Borate suggests, check you don't have any tiny clip bits that may not be seen in timeline mode...they can cause puzzling things to happen.
Nat