What is the ruling on seeking forgiveness ten thousand times a day without the desired outcome being achieved, and do you advise to continue?

It is desirable to increase seeking forgiveness (Istighfar) without specifying a certain number. If a number is specified, there is no harm in it, as long as its virtue or Sunnah status is not believed, and this would be for the purpose of time management and consistency.

One should increase in seeking forgiveness and supplication (Du'a) without haste, and with good a opinion of Allah. For Allah answers supplications, and the answer may come by expediting what is requested, or by saving it for the Hereafter, or by averting evil. Acceptance may be delayed due to hindrances such as not seeking lawful (halal) sources for food, drink, and clothing, or supplicating for sin or the severance of kinship ties, or due to haste.