Reusable water bottles have a higher failure rate than other containers, but they are reliable enough for short trips, and bringing 2 or 3 in case 1 fails should be reliable enough even on medium-length trips.
I go through a lot of bottles of water, I would estimate thousands of them per year, as I am supporting a family of 6 on a daily basis and some other people intermittently and everyone in the family drinks a lot of bottled water with some of us trying to reuse them when we remember to do so. Therefor, the high rate of failures I note below is partially due to the volume of bottles used being much higher than your normal person or family. Also, we are not careful with them, so they take a beating.
First, don't buy the super cheap reusable plastic bottles
Beware of the super cheap, plastic, reusable bottles, as some of them are junk and should be expected to break on the first or second outing if not handled with extreme care. I am not even considering the ones that you can get for a buck or two on the discount shelf.
Disposable water bottle failure
I have had disposable water bottles fail for me many times and in various ways. Leaks due to improper sealing at the cap, leaks in any random place due to tears or tiny holes, catastrophic tears that immediately empty the container, etc.. There are a variety of ways they can go bad.
I would say disposable bottle failure rate per bottle for non-reused bottles is way less than 1%. But I do reuse a lot of them, sometimes for a week or two. When heavily reusing, I would estimate that the failure rate is greater than 1%, but I don't keep track and cannot specify how much greater. Probably less than 10% though.
Reusable bottle failure
We have also used a lot of permanent, reusable water bottles, and we have had problems with those as well. Some of the problems are the same or similar: leaks due to bad seals at the cap, catastrophic destruction from bottles tearing or crushing, and tiny holes in some of the flexible plastic containers.
That said, I would estimate that the failure rate for the permanent bottles was lower than the failure rate for the disposable bottles. Disposable bottles are not made to be quite as tough, so they fail more often.
I'm not sure what the upper limit is on my reuse of disposable bottles, as I don't keep track, but more often than not I replace them because I was in a situation where I could just grab up another new one, not because the old one broke. That is anecdotal evidence that they can usually be reused a bunch of times without failing.
If you are going out for an ultra-light trip for a weekend, reusing disposable water bottles should be fine. I have done this, and I have reused the same water bottle for a week or two. If you are going out for more than 1 day, I would highly recommend that you bring at least 2 of them, even if you plan to be able to refill them often, just to be safe in case one does malfunction. Though malfunctions are not common, they happen at least enough that I would not risk being out with only 1.
If you do not need ultra-light, I would recommend a permanent steel bottle. I have had malfunctions even with them, but it is far less often. I have had leaks at the seals even on metal bottles, and I have dented and punctured them. However, dents and punctures in steel bottles is usually due to some form of damage that would have obliterated some lesser bottle. Even when dented, they still work great as long as they are not leaking; I had a steel bottle I used for a while even with a big dent in it. Be careful though of points in dented steel bottles being sharp enough to cut through your pack, or even cut you, if the ends of the dent are bent sharply enough. My preference is the ones you can also cook in, not the drinking-only ones that have paints on them and might be lined with other materials.
Another benefit of bringing 2 disposable water bottles instead of 1 reusable one on a trip is that, even though each disposable is more likely to fail on its own, I would say that having multiple disposable bottles all fail on 1 trip is probably less likely than having the 1 reusable bottle fail. So 2 or 3 disposables is likely more reliable than 1 reusable.
The failure rate is low enough when reusing disposable water bottles that you can do it for days, often even weeks. But the failure rate is high enough that it would be unwise to trust your hydration to only 1 of them. If the trip is longer than a day, bring at least 2, and if the trip is for weeks, bring even more than 2.