Should I give him time?

I'm asexual and my husband of 12 years is very torn between staying or starting a new. I'll start of with we have so much in common from hobbies to moral compass we share same core values. But 5 years ago I got into this depression because he put me in a bubble where I felt like I had to rely on him for everything. I'm literally like a princess..then I became lazy no motivation but I was studying at the time. So I was looking forward to that and entering the work force fast forward to my graduation he convince me to not get a job and just stay at home, his reasoning was "because our love would grow apart" so I stayed at home it became really bad I had no motivation, and ambition I felt like I was living this life of serving him. I felt like a leach providing for us. Then he emotionally cheated because I neglected US. Then I just became resentful while trying to mend our marriage. But somewhere along the line he started asking me to get a job since we moved to a new city where living expenses is high. I had to power through that to push my self to find a job. And that also brought back my motivation. Since I am asexual we compromise on sexual activity and this 1 session we did that involve a pill got me down and I was back on being unmotivated but I try really hard to push through at least my study to get a job. But now he is unsure of what to do. I 2day I told him I'm letting go since. But he wants me to stay while he's indecisive. He said he will rather be lost than loose me.