I see, but what I am really trying to wrap my head around is why the tanto is ignored after the first strike.
You have some very good questions that I think are important for those who have the power to adapt their training to deal with more than just sport applications.
In shiai when one is struck with the tanto it has to be done in a particular manner. Eddy identified the requirements for a "correct" tanto strike in shiai above. The concept of ki ken tai no itchi is critical in this regard as the tanto thrust must be done with a step from the correct distance with the thrusting arm parallel to the floor and will not count as a strike (under competition rules) if one simply stabs from zero range after closing on the other player. In this light the thrust is more along the lines of European fencing than tanto jutsu per se.
Does this make sense from a modern knife fighting or self defence perspective - absolutely not imho. When one gets stabbed in competition it is more of a penalty against Toshu (the unarmed player) for non-existent tai sabaki instead of a reward to Tanto (the armed player) for having stabbed the other person. In the sense of Aikido fundamentals it makes sense that if one can't avoid being hit then the possibility of executing any technique becomes practically impossible.
Why keep the form of knife fighting for the first strike and then switch to unarmed tactics without a definite disarm as apposed to keep treating the attacker like they are armed or constantly treating the uke as they are unarmed, I guess would be my question.
As indicated by others, it should not be common practice to disregard the importance or existence of the tanto. But it is important to note that although there is a tanto in the match, there is not much of actual knife fighting tactics or techniques being used. As I said earlier, the primary role of the tanto is to enforce distance to minimize the possibility of an Aikido match turning into a Judo and grappling match. Tomiki was a high level Judoka and many of the early members of the Waseda Aikido Club (his first dojo where he developed the shiai system) were judoka. As a result the problem of matches becoming close range Judo bouts was a real issue. The tanto was introduced to prevent this problem.
In shiai when distance is closed after the initial strike it is Tanto's duty to place the knife on the chest or shoulder of Toshu if he is attempting a technique. This is to remind Toshu that he can be stabbed at this range and has to deal with the knife before technique can be attempted. Usually in shiai if Toshu applies an effective technique but had ignored the knife being pressed against his chest, the technique is disallowed. I believe the rules state that if Toshu ignores the knife pressed to his chest for more than 5 seconds he gets a warning and the 2 players are broken up and the bout is restarted from distance.
I think this is a good thread because many are unable to understand the difference between tanto shiai and Aikido self defence applications against tanto. It is something to be considered because meeting a trained knife fighter (especially of the FMA ilk) is nothing like Tanto Shiai and requires a pretty specific skill set imho.