要解决Android GridView滚动后不保持选中状态的问题，可以使用以下方法：

1. 在适配器中记录选中的项的位置，并在getView方法中根据该位置设置选中状态。

public class GridViewAdapter extends BaseAdapter {
    private Context mContext;
    private List mData;
    private int mSelectedPosition;

    public GridViewAdapter(Context context, List data) {
        mContext = context;
        mData = data;
        mSelectedPosition = -1;
    }

    public void setSelectedPosition(int position) {
        mSelectedPosition = position;
        notifyDataSetChanged();
    }

    @Override
    public int getCount() {
        return mData.size();
    }

    @Override
    public Object getItem(int position) {
        return mData.get(position);
    }

    @Override
    public long getItemId(int position) {
        return position;
    }

    @Override
    public View getView(int position, View convertView, ViewGroup parent) {
        ViewHolder holder;
        if (convertView == null) {
            convertView = LayoutInflater.from(mContext).inflate(R.layout.grid_item, parent, false);
            holder = new ViewHolder();
            holder.textView = convertView.findViewById(R.id.text_view);
            convertView.setTag(holder);
        } else {
            holder = (ViewHolder) convertView.getTag();
        }

        holder.textView.setText(mData.get(position));

        // 设置选中状态
        if (position == mSelectedPosition) {
            holder.textView.setBackgroundColor(Color.RED);
        } else {
            holder.textView.setBackgroundColor(Color.WHITE);
        }

        return convertView;
    }

    private static class ViewHolder {
        TextView textView;
    }
}

2. 在Activity中监听GridView的滚动事件，并在滚动时记录当前选中的位置。

public class MainActivity extends AppCompatActivity {
    private GridView mGridView;
    private GridViewAdapter mAdapter;
    private int mLastVisiblePosition = -1;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mGridView = findViewById(R.id.grid_view);
        List data = new ArrayList<>();
        for (int i = 0; i < 100; i++) {
            data.add("Item " + i);
        }
        mAdapter = new GridViewAdapter(this, data);
        mGridView.setAdapter(mAdapter);

        mGridView.setOnScrollListener(new AbsListView.OnScrollListener() {
            @Override
            public void onScrollStateChanged(AbsListView view, int scrollState) {
                // Do nothing
            }

            @Override
            public void onScroll(AbsListView view, int firstVisibleItem, int visibleItemCount, int totalItemCount) {
                // 记录最后一次可见的位置
                mLastVisiblePosition = firstVisibleItem + visibleItemCount - 1;
            }
        });

        mGridView.setOnItemClickListener(new AdapterView.OnItemClickListener() {
            @Override
            public void onItemClick(AdapterView parent, View view, int position, long id) {
                mAdapter.setSelectedPosition(position);
            }
        });
    }

    @Override
    protected void onResume() {
        super.onResume();
        // 恢复选中状态
        if (mLastVisiblePosition >= 0) {
            mAdapter.setSelectedPosition(mLastVisiblePosition);
        }
    }
}

通过以上方法，当GridView滚动后，选中的项会保持选中状态。