There's really two issues here. The first is a scientific question, and not a philosophical one. The second is a matter of philosophy, specifically epistemology (the study of knowledge).
1. Scientific Question: At what point would life be too complex for evolution by natural selection to realistically account for it?
If the complexity and specific structures observed appeared too early in the history of life to be compatible with biological possibility. Biological possibility would be related to things like mutation rate, population size and geographical distribution of species, average generation time, etc.
So, to take an absurd example, evolution by natural selection would not account for an observation of Homo sapiens appearing during the time of only bacteria and archebacteria, billions of years ago. Less absurd might be if we observed a brain with mammalian complexity from an annelid nervous system, evolving in 5,000 years--still far too short a time for that to occur by evolution alone.
The vast majority of biologists think life has had sufficient time to evolve to where it is now. To give detailed explanations of it all would be beyond the scope of a philosophy post. But it might be helpful to briefly underscore the magnitude of the amount of time and the amount of biological interactions that have happened since life began.
We tend to forget that many of the structures found in life (proteins, phospholipids, etc.) evolved in bacteria, and bacteria have a generational time on the order of a half hour to a day. Let's say it's a half day for convenience. That means each day there are two generations of bacteria if you start with one cell. Each year, 730 generations. The 1.5 billion years of bacterial life, that's over a trillion generations. If it were once every half hour, it'd be 26 trillion generations.
But it's far more extreme than even that, since mutations are happening in parallel, meaning that there are unimaginable numbers of bacteria out in the world at any given time (one estimate puts it currently at "five with 30 zeroes after it") , all of which can be candidates for producing new traits.
In fact, an actual experiment in a lab saw an important new trait evolve in E. coli in "just" ~30,000 generations.
2. Epistemological Question: Should we accept explanations without evidence?
One way to look at this issue is reforming the question to be, "Is it ever warranted to default to Explanation B, for which we have no evidence, just because Explanation A fails?"
That question reduces to this question: "Is it ever warranted to accept an explanation without any evidence in favor of it?"
The answer to that is a huge area in epistemology, beyond the scope of a single SE answer. But you can start with the idea of "Foundationalist Theories of Epistemic Justification" to explore why we have warrant to accept any belief.
But to explore that issue in this context, let's assume for the sake of argument that we decide that the complexity in nature means evolution by natural selection fails as an explanation. In this case, filling that in with these particulars would give us, "Is it ever warranted to default to Intelligent Design as an explanation, for which we have no evidence, just because evolution by natural selection fails as an explanation?"
I tend to work under the rule that one does need evidence in order to hold a belief about the physical nature of the world. Therefore, I don't think it is a good idea to default to intelligent design.
Instead, what we should do at that point is (given this hypothetical where we decide evolution fails as an explanation) simply admit we don't know what explains the complexity in nature.
Let me push this envelope even further. Let's assume that next year, a geneticist noticed that on human chromosome 17 there is a sequence of base pairs that, if interpreted through the right decoding rules, spells out a 20,000 word message in English, something to the effect of, "I am the Intelligent Designer, and I designed you. Here are my instructions for life...". Assume the story is not fake and the research is done extremely rigorously and is reproduced by dozens of honest top scientists.
Would we then have warrant to accept with absolute certainty that there is an Intelligent designer behind the complexity of life? At first, it would seem like it, but then consider other similarly evidence-less explanations:
- The human mind somehow has causal power over the genetic code and there is some collective unconscious that is programming that into us.
- Rogue scientists created this DNA sequence in the early 2000s and disseminated it via a highly contagious virus that incorporated the sequence into everyone's DNA within a few years.
- Time traveling scientists/aliens did this to us at some time in the past 2000 years.
- It turns out to be proven that every sequence of any 20,000 word book can be found in the DNA if you use a supercomputer to find the right decoding rules.
These seem far-fetched, but are they any more far-fetched than the idea of what amounts to a magic person doing this merely by thinking about it?