WordPress runs on a MySQL database, which can handle many millions of records.
However, when it comes to importing multiple thousands of records, PHP has a memory limit that means in practice, you have to break up your data imports into batches of approximately 5000 records.
Also, some managed hosts arbitrarily kill PHP processes at a certain timeout to ensure their servers aren’t overloaded.
If you have 5000+ records, please contact Tech Support and we will help you with your import.
Presspoint will tell you how much memory it used during any particular import, so you can calculate the optimum batch size