This is called the "waiver trap," and it can be quite harsh indeed.
Rule 8 and Rule 12 require a defendant to assert most affirmative defenses almost immediately -- either in their answer or in either a motion to dismiss or a motion for judgment on the pleadings. Failure to assert them does indeed result in a waiver of the defense.
For instance, in Hunter v. Serv-Tech, the defendant filed a motion to dismiss based on defects in service of the complaint. The defendants' motion purported to "reserve the right" to challenge personal jurisdiction, as well, but did not actually move for dismissal on that basis. After the service issue was resolved, the defendants actually moved to dismiss based on personal jurisdiction, but the court denied the motion, saying that Rule 12 requires an actual assertion and argument in support of the defense:
The Court is aware that the outcome it reaches today is a harsh one, especially in light of the fact that it appears that, absent waiver, this motion might well be granted. But the Court is duty-bound to apply the law as it is written, and as written the Rules enact a policy of requiring all 12(b)(2)-(5) defenses to be made by motion, once, prior to filing an answer. Given this policy, Offshore’s “reservation” language is not sufficient to preclude waiver.
So the court acknowledges that the defendant had a winning defense, but it must nonetheless continue to litigate.
The rule is applied quite strictly in cases involving Rule 12(b)(2)-(5) defenses. There is quite a bit more wiggle room for other affirmative defenses, i.e., defenses that allow the defendant to escape liability regardless of whether his conduct was wrongful, but it still remains quite dangerous to omit any available defense from your first responsive pleading. See, e.g., Am. Nat. Bank of Jacksonville v. Fed. Deposit Ins. Corp., 710 F.2d 1528, 1537 (11th Cir. 1983) ("In any case, we need not consider these points since SFC waived its right to advance the statute of limitations defense by its failure to assert this affirmative defense in any pleading filed below in compliance with Fed.R.Civ.P. 8(c).").
As a practical matter, then it is not usually sufficient to simply say "I disagree" in response to a claim, unless your defense amounts to either a denial that the facts supporting the claim are true or a denial that the facts as alleged creates a cause of action. If you intend to assert an affirmative defense – such as personal jurisdiction, statute of limitations, failure of consideration, accord and satisfaction, immunity, etc. – you must say so clearly.
So if your first responsive pleading is an answer, it is typically sufficient to simply say, "The claim is barred by the statute of limitations." But if your first responsive pleading is a motion to dismiss, you need to both assert and argue your defense; otherwise, you risk waiving it as in Hunter.
Note, though, that there are some affirmative defenses that are not waived by failing to assert them immediately. Failure to join a necessary party, for instance, can be asserted at any time up until trial, and subject-matter jurisdiction can be raised at basically any time at all.