I have had the exact same issue as you for years on a number of different horns. The issues is that the 1st valve gets the most moisture and debris build up since it is the 1st in the airstream. This both washes out the Blue Juiice quicker and also builds up a lime/calcium deposit quicker which makes the valve feel dry and sticky when the valve oil gets thin.
1. The horn should NOT be stored "on the bell" with the bell pointing down. This causes all the bad stuff to drain back into the valves. Ideal is store the horn on a euphonium stand with bell point straight up. Even sideways in the case is not ideal, but if you do store in the case, have the leadpipe and bell up and 3rd valve down. The least amount of goup will collect in the 1st valve this way.
2. Take the 1st valve out (and spring and bottom cap) and "snake" the leadpipe from the inside (valve) toward the receiver. I use a brass-saver swab for this. This removes crud from the leadpipe which often is the most common source of goup.
3. I not only clean my 1st valve more frequently, but every once in while (2 months or so) I use a very fine silver polish (Wrights Silver Cream) to LIGHTLY polish and remove the built up lime scale on the surface of the valve. This is the most common reason for the "dryness" that you experience. Wash the valve off thoroughly after this!!!
4. Blue Juice will wash out quite quickly in the 1st valve (which gets the most direct moisture). Occasionally (once every 1-2 weeks) I use a valve oil that leaves more residue on the valve such as Hetman #1 when I put the horn away. This doesn't dry out the way Blue Juice does. Then I use Blue Juice thereafter to get the slick smooth action i like.
Adams E3 0.60 Sterling bell - Prototype top sprung valves
Concord Band
Winchendon Winds
Townsend Military Band