Israel would like peace, but they know it's not feasible. Peace will only come about either with the at a minimum extirpation of Jews from the area, or with th

Israel would like peace, but they know it's not feasible. Peace will only come about either with the at a minimum extirpation of Jews from the area, or with the backers deciding they don't want to support the war anymore--and that would require at a minimum a serious threat of Israel going nuclear, probably actually nuking somebody's capital. Hence the low-level conflict is the least bad choice.