Flash memory stores the information as electric charge (electrons for negative charge, or lack of electrons for positive charge) in a buried and insulated (in oxide) gate of a mosfet transistor. Once this charge is transferred into that gate, it can stay there for a period of time expressed in years, or tens of years, and it can still be read correctly as 1 or 0. This is called RETENTION time. After that period, the charge wil statistically leak out and be insuficient for that bit of information to be read correctly. Depending on the technology, a bit of information is stored as no charge (logic level 1, or bit 1), while the other (logic level 0, or bit 0) as charge present in the transistor, so after the retention time only the logic level 1 will be ready correctly, because there was no charge to leak out. Anyways, that's irrelevant, if some of the 0 bits are not read, the information is lost. For flash memory this time is 10 years as guarantied retention time, for eeprom is 100 years in normal storage conditions. Temperature affects the retention, higher temperature leads to higher leakage of charge from that insulated gate, so better keep the flash cards cool.
Now, to answer your question, powering up the drive containing that memory does not refresh it's content. You can keep it powered up continuously, the information stored in the transistors is NOT UPDATED OR REFRESHED by the power applied to device, unless you write again the information. This principle of refreshing the data from time to time is used in the RAM memory in computers, and losing power leads to losing data.
Hard drives based on magnetic retention of data are better in this respect, since the retention time is greater if the device is kept properly.
Another thing about the flash memory is the indurance of the cell, how many times the memory cell accepts write/erase cycles until it starts to "wear" and not store anymore the information. That number is in the hundreds now days. If you read correctly the specification of an SSD drive, you will find a specification called "TBW", total bytes written. Dividing that number by the capacity of the drives yields the number of erase/write cycles that will wear the cells.
Flash memory based drives have now implemented a special "wear" algorithm, such that new data is written on cells that are not progammed with data, and so files are moved continuosly across the drive to mentain a balance of erase/program for all the cells, otherwise if a file is continuously written and modified on the same memory cells, these will wear after those few hundred of cycles and not be able to be used anymore. That is why a worn out SSD drive, that has reached a TBW spec, will not retain the information for long.