I think both situations are vices/virtues related. Check your general's vices&virtues descriptions.
1. Your general is probably a kind of "poor attacker".
2. High valor sometimes is not enough. There are many vices that reduce units' morale.

Do not let the general get any vice. To avoid this don't keep your general in command of full stack. Generals commanding a lot of soldiers get vices very often (especially when they stay in one province for several years). If you keep stacks commanded by non-star generals, it's less likely that the random vice will spoil your precious 9 star general. Try to switch generals/governors between provinces from time to time. It should help with "lazy" kind of vices too.