Laches is an equitable defense. It therefore depends on there having been an unreasonable delay, which harmed the party asserting the defense. What is reasonable is determined by the court in each case,there is no set time period, but a delay significantly longer than would occur in the normal course of business, without a good reason, may well be found unreasonable. "I made a mistake" is not generally considered a good reason.
However, the party asserting laches must have been harmed or prejudiced by the delay. Common sources of such prejudice are witnesses or evidence being lost or hard to locate because of the delay, and the party affected by the delay having made significant choices whch s/he would have made otherwise had that party known of the legal claim.
The party asserting laches has the burden of showing the delay, showing that it is unreasonable, and showing that s/he was prejudiced by the delay. That party must indicate why it would be unfair to allow the claim after the delay.
Laches is an equitable defense. Therefore it is normally asserted when the plaintiff seeks an equitable remedy, such as an injunction. It is often not available as a defense to an action for money damages, although this may vary by jurisdiction. In a money damages case, a statute of limitations will often apply, instead.
Also, as an equitable defense, laches will generally be available only in common-law legal systems that include the English equity courts in their ancestry.
If the parking space rental was not included in the lease or other written agreement which the tenant signed or accepted, it is hard to see on what ground the tenant can be claimed to owe such a fee at all.
If the tenant did agree to the fee, bu twas never notified of any increase, it is hard to see a legal basis to charge the larger fee.
In many jurisdictions, if the landlord accepts rent payment without complaint, or does not complain within one rental period (often a month) it may waive any claim that the rent paid was too little.
The statute of limitations may bar claims more than a certain number of year ago, the number dependent on the jurisdiction.
A tenant in such a situation might be wise to consult a lawyer with expertise in landlord/tenant law in that jurisdiction before going to court.
The LII page "Laches" reads:
laches [is] [a] doctrine in equity that those who delay too long in asserting an equitable right will not be entitled to bring an action.
The Wikipedia article "Laches (equity)" reads:
Invoking laches is a reference to a lack of diligence and activity in making a legal claim, or moving forward with legal enforcement of a right, in particular with regard to equity, and so is an "unreasonable delay pursuing a right or claim, in a way that prejudices the [opposing] party". When asserted in litigation, it is an equitable defense, that is, a defense to a claim for an equitable remedy. The essential element of laches is an unreasonable delay by the plaintiff in bringing the claim; because laches is an equitable defense, it is ordinarily applied only to claims for equitable relief (such as injunctions), and not to claims for legal relief (such as damages). The person invoking laches is asserting that an opposing party has "slept on its rights", and that, as a result of this delay, witnesses and/or evidence may have been lost or no longer available, and circumstances have changed such that it is no longer just to grant the plaintiff's original claim...
... Even if the court denies equitable relief to a plaintiff because of laches, the plaintiff may still have a claim for legal relief if the statute of limitations has not run out.
Under the United States Federal Rules of Civil Procedure, laches is an affirmative defense, which means that the burden of asserting laches is on the party responding to the claim to which it applies.
The Thomson Reuters Practical law page "Laches" reads:
Laches is an equitable defense, or doctrine. A defendant who invokes the doctrine is asserting that the claimant has delayed in asserting its rights, and, because of this delay, is no longer entitled to bring an equitable claim. Failure to assert one's rights in a timely manner can result in claims being barred by laches: it is a maxim of equity that, "Equity aids the vigilant, not the negligent."
However, delay alone is not enough to prevent a claimant obtaining relief. The consequence of the delay must be that it would be unfair for the court to give relief, usually because the defendant has changed its position because of the delay.
The party asserting laches has the burden of proving that it is applicable. Laches is distinguishable from the statute of limitation, which prevents a party from asserting claims after the designated limitations period has expired.
 Garner, Bryan A., ed. (2009). "Laches [Definition of 'laches' by Black's]". Black's Law Dictionary (9th ed.)
 Bray, Samuel (2014). "A Little Bit of Laches Goes a Long Way: Notes on Petrella v. Metro-Goldwyn-Mayer, Inc" (PDF). Vanderbilt Law Review en Banc. 67: 1–18.