The downside of Kat's power is that she can't remember anything beyond 3 months (roughly). But how does her memory loss work, does she lose an hour, day or week at a time or do her memories just sort of fade over time?
tl;dr: her memories "fade" gradually over the course of approximately 30 days. That does not appear to be an exact number, but rather the typical amount of time it takes for her to forget something if she doesn't constantly try to re-learn it. She has never described her memory loss in abrupt or specific terms.
After she describes her memory loss to Rosen, he explains it's physiology in terms of transferring memory from short-term to long-term storage. In practice(*), short-term memory storage lasts for a matter of seconds, at which point information is either stored permanently in long-term memory or forgotten.
It appears as of Kat's long-term memory behaves much like her short-term memory, just over a longer period. Things that she is continuously thinking about, or refreshing, stay in her mind, while everything else fades. For example, she hasn't forgotten the identities of the rest of the Alpha team, nor the fact that Dr. Rosen wants her to video tape her life, because those things are likely in the front of her mind on a regular basis. On the other hand, she's already had to write down memories from her first episode, because she is not continuously thinking about those events and so they fade. This is similar to a form of anterograde amnesia, though again on a much longer scale.
It's not clear how much her memory loss it related to her ability to retain new information. It's possible that her mind works much like @TeamGB's answer describes: she loses old information as new information arrives. However, we haven't seen enough of her history to know if that pattern holds true; she describes her own memory loss in terms of time, not volume of information, but then again she can't remember anything so she may be wrong. However, I think that it's probably not that simple. In particular, we know that her long-term memory is intact, she just has no access to it. Nina was able to recover a memory of Kat's mother, which Kat later used to draw a picture, implying that the memory had be fully recalled into her "active" memory storage. How much of her accumulated lost memories can be recovered is likely going to be a focus of her character arc over the rest of the season.
In exchange for a failing long-term memory, she has a nearly-perfect "muscle memory", where she can "store" remembered actions without having to actually perform the physical act. (This is similar to Monica Dawson from Heroes or Marvel villain TaskMaster). Unlike her mental memories, her muscle memory never fades. She has accumulated a whole array of skills that she cannot remember learning, but can perform flawlessly anyway. It does not appear that this muscle memory acquisition directly affects her long-term memory -- learning new skills doesn't seem to change how fast her memories fade. The two effects likely have a similar root cause, but otherwise act independently.
(*) We really don't know as much as we'd like about the biology of human memory; this is a simplified description of the most popular theory of memory storage, but there are many psychologists that dispute it. This not legal advice; please consult your doctor; etc.
For what I can gather from watching the show. Her mind can almost be seen as a queue and when she learns so many new things the last thing she remember i.e. the memory at the top of the queue is pushed off so forgotten. To answer your question I think if she didn't learn such a lot of new things in a short time her memories might keep for longer. So they fade over time
A very quick snip in the other days episode was where she beat Bill in a fight. She should have forgotten that by now but she wrote it down haha. So this memory had already faded.
UPDATE After the other nights episode where Mitchell tried to access her memories, all that was left was a advert for some cleaning. This shows that something has happened to her long term memory. However there is still not enough proof to correctly identify is her long term memory get completely destroyed. As she did manage to remember it, even if it was not what she wanted to remember.