I think it was correct you couldn't reshuffle the stack in your solo game.
From the rules:
"Set up: Shuffle the Construction cards and create two equal stacks. Compose a unique stack of Construction cards by adding the Solo card to one of the two stacks then putting this stack under the other. ... When the Solo card is picked, all the Plans are considered as "approved" by the competition and it is no longer possible to get the higher score."
So reshuffling would reduce your chances to get the higher score for the other 2 plans.
Also from the rules:
"The game ends when the stack of card is empty, or one of the three end conditions of the basic version occurs."
I understand this as the solo game is meant to play only once through all the cards. Reshuffling might allow you to play a longer game (as you said).
Due to these two rules, the solo game were some more luck based, if you could reshuffle. I think instead it should rather measure your skills under similar conditions. So I consider this neither a bug nor a mistake.
I don't understand why you said you "lost by running out of cards". The solo game is played for your personal high score and is considered a win by BGA.
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